Below is a complete set of 250 practice questions—with their answers—divided into five categories. Each category focuses on a specific type of expression or word‐problem, progressing from basic arithmetic to more involved nested expressions and word‐problem translations.
Category 1: Basic Simplification Problems
(Simple expressions with two or more operations, no or minimal use of brackets)
- 15 − 7 + 4
Answer: 12 - 18 ÷ 2 + 4 × 2
Answer: 17 - 6 + 8 − 3
Answer: 11 - 10 × 2 − 5
Answer: 15 - 24 ÷ 4 + 3
Answer: 9 - 12 + 6 ÷ 3
Answer: 14 - 5 × 3 + 10
Answer: 25 - 20 − 4 × 2
Answer: 12 - 16 ÷ 2 − 3
Answer: 5 - 9 + 7 − 4
Answer: 12 - 8 × 3 − 10
Answer: 14 - 30 ÷ 5 + 7
Answer: 13 - 25 − 10 + 5
Answer: 20 - 14 + 8 ÷ 4
Answer: 16 - 7 × 2 + 3
Answer: 17 - 50 − 25 + 10
Answer: 35 - 18 + 12 − 6
Answer: 24 - 27 ÷ 3 + 4
Answer: 13 - 4 + 9 − 2
Answer: 11 - 10 − 3 + 8
Answer: 15 - 6 × 2 + 4
Answer: 16 - 20 ÷ 4 − 2
Answer: 3 - 15 + 5 − 10
Answer: 10 - 3 × 4 + 2
Answer: 14 - 32 − 16 + 8
Answer: 24 - 40 ÷ 5 + 6
Answer: 14 - 9 + 12 − 7
Answer: 14 - 14 − 2 + 10
Answer: 22 - 6 × 3 − 5
Answer: 13 - 20 + 10 − 8
Answer: 22 - 8 × 2 + 3
Answer: 19 - 36 ÷ 6 + 7
Answer: 13 - 18 − 4 + 9
Answer: 23 - 7 + 6 × 2
Answer: 19 - 50 − 10 ÷ 2
Answer: 45 - 15 ÷ 3 + 8
Answer: 13 - 9 + 5 × 2
Answer: 19 - 28 − 7 + 3
Answer: 24 - 16 ÷ 4 + 6
Answer: 10 - 12 + 14 − 9
Answer: 17 - 4 × 3 + 7
Answer: 19 - 30 − 5 + 2
Answer: 27 - 20 ÷ 2 + 1
Answer: 11 - 11 + 9 − 5
Answer: 15 - 18 − 2 + 4
Answer: 20 - 6 + 5 × 2
Answer: 16 - 24 ÷ 3 + 8
Answer: 16 - 7 + 8 − 3
Answer: 12 - 10 + 4 − 2
Answer: 12 - 9 × 2 − 5
Answer: 13
Category 2: Expressions with Brackets
(Expressions using a single set of brackets to enforce the order of operations)
- 9 − (4 + 2)
Answer: 3 - 24 ÷ (8 − 5)
Answer: 8 - 8 × (5 − 2)
Answer: 24 - 7 + (12 − 5)
Answer: 14 - (15 − 7) + 4
Answer: 12 - 20 − (3 + 2)
Answer: 15 - 18 ÷ (6 − 3)
Answer: 6 - 10 × (8 − 3)
Answer: 50 - 30 ÷ (10 − 7)
Answer: 10 - (5 + 3) × 2
Answer: 16 - 14 − (2 + 3)
Answer: 9 - (18 − 9) + 4
Answer: 13 - (20 + 5) − 8
Answer: 17 - 16 ÷ (8 − 4)
Answer: 4 - 7 × (9 − 6)
Answer: 21 - 50 − (30 ÷ 5)
Answer: 44 - (12 + 8) ÷ 4
Answer: 5 - 9 + (7 − 3)
Answer: 13 - 10 − (2 + 3)
Answer: 5 - 15 ÷ (5 − 2)
Answer: 5 - 24 − (6 + 2)
Answer: 16 - (20 − 5) + 3
Answer: 18 - 18 ÷ (9 − 6)
Answer: 6 - 7 + (12 ÷ 4)
Answer: 10 - 14 − (9 − 4)
Answer: 9 - (8 + 2) × 3
Answer: 30 - 27 ÷ (9 − 6)
Answer: 9 - 16 + (12 − 8)
Answer: 20 - (25 − 10) + 7
Answer: 22 - 18 − (3 + 4)
Answer: 11 - 20 ÷ (10 − 5)
Answer: 4 - (14 + 6) − 5
Answer: 15 - 8 × (7 − 3)
Answer: 32 - 12 − (6 ÷ 2)
Answer: 9 - (9 + 6) ÷ 3
Answer: 5 - 30 − (10 + 5)
Answer: 15 - 15 + (20 − 5)
Answer: 30 - (16 − 4) + 2
Answer: 14 - 42 ÷ (7 − 3)
Answer: 10.5 - 10 × (3 + 2)
Answer: 50 - (50 − 30) ÷ 4
Answer: 5 - 25 − (10 + 3)
Answer: 12 - (20 ÷ 2) + 6
Answer: 16 - 14 + (8 − 3)
Answer: 19 - (30 − 10) ÷ (5 + 5)
Answer: 2 - 18 − (8 ÷ 2)
Answer: 14 - (15 + 5) − (9 − 3)
Answer: 14 - 12 × (6 − 4)
Answer: 24 - (21 − 7) + (8 − 3)
Answer: 19 - 28 ÷ (12 − 8)
Answer: 7
Category 3: Complex Expressions with Multiple Brackets
(More challenging problems with nested brackets of various types)
- 25 − [20 − {10 − (7 − 5 − 3)}]
Inside: (7−5−3) = –1; {10 − (–1)} = 11; [20 − 11] = 9
Answer: 25 − 9 = 16 - 100 − 3 [20 + {50 − 40}]
Inside: {50−40} = 10; [20+10] = 30; 3×30 = 90
Answer: 100 − 90 = 10 - 50 − [20 + {30 − (20 − 5)}]
Inside: (20−5) = 15; {30−15} = 15; [20+15] = 35
Answer: 50 − 35 = 15 - 40 − {15 − [8 − (3 − 1)]}
Inside: (3−1) = 2; [8−2] = 6; {15−6} = 9
Answer: 40 − 9 = 31 - 60 ÷ [12 − {4 + (3 − 1)}]
Inside: (3−1) = 2; {4+2} = 6; [12−6] = 6
Answer: 60 ÷ 6 = 10 - 30 − {20 − [15 − (8 − 3)]}
Inside: (8−3) = 5; [15−5] = 10; {20−10} = 10
Answer: 30 − 10 = 20 - 80 − [50 − {30 − (20 − 10)}]
Inside: (20−10) = 10; {30−10} = 20; [50−20] = 30
Answer: 80 − 30 = 50 - 90 − {60 − [40 − (25 − 15)]}
Inside: (25−15) = 10; [40−10] = 30; {60−30} = 30
Answer: 90 − 30 = 60 - 75 − [30 + {20 − (10 − 5)}]
Inside: (10−5) = 5; {20−5} = 15; [30+15] = 45
Answer: 75 − 45 = 30 - 100 − {50 − [30 − (12 − 7)]}
Inside: (12−7) = 5; [30−5] = 25; {50−25} = 25
Answer: 100 − 25 = 75 - 55 − [25 − {15 − (10 − 5)}]
Inside: (10−5) = 5; {15−5} = 10; [25−10] = 15
Answer: 55 − 15 = 40 - 68 − {30 − [18 − (9 − 3)]}
Inside: (9−3) = 6; [18−6] = 12; {30−12} = 18
Answer: 68 − 18 = 50 - 90 − [45 − {20 − (12 − 8)}]
Inside: (12−8) = 4; {20−4} = 16; [45−16] = 29
Answer: 90 − 29 = 61 - 120 − {60 − [30 − (15 − 5)]}
Inside: (15−5) = 10; [30−10] = 20; {60−20} = 40
Answer: 120 − 40 = 80 - 100 − [40 − {25 − (10 − 2)}]
Inside: (10−2) = 8; {25−8} = 17; [40−17] = 23
Answer: 100 − 23 = 77 - 84 − {36 − [18 − (9 − 3)]}
Inside: (9−3) = 6; [18−6] = 12; {36−12} = 24
Answer: 84 − 24 = 60 - 70 − [30 − {20 − (11 − 6)}]
Inside: (11−6) = 5; {20−5} = 15; [30−15] = 15
Answer: 70 − 15 = 55 - 66 − {33 − [18 − (7 − 2)]}
Inside: (7−2) = 5; [18−5] = 13; {33−13} = 20
Answer: 66 − 20 = 46 - 95 − [50 − {30 − (14 − 6)}]
Inside: (14−6) = 8; {30−8} = 22; [50−22] = 28
Answer: 95 − 28 = 67 - 88 − {44 − [22 − (11 − 3)]}
Inside: (11−3) = 8; [22−8] = 14; {44−14} = 30
Answer: 88 − 30 = 58 - 110 − [70 − {40 − (15 − 5)}]
Inside: (15−5) = 10; {40−10} = 30; [70−30] = 40
Answer: 110 − 40 = 70 - 130 − {80 − [50 − (20 − 10)]}
Inside: (20−10) = 10; [50−10] = 40; {80−40} = 40
Answer: 130 − 40 = 90 - 75 − [25 + {15 − (8 − 3)}]
Inside: (8−3) = 5; {15−5} = 10; [25+10] = 35
Answer: 75 − 35 = 40 - 100 − {55 − [30 − (18 − 8)]}
Inside: (18−8) = 10; [30−10] = 20; {55−20} = 35
Answer: 100 − 35 = 65 - 60 − [20 + {15 − (7 − 2)}]
Inside: (7−2) = 5; {15−5} = 10; [20+10] = 30
Answer: 60 − 30 = 30 - 90 − {40 − [20 − (10 − 4)]}
Inside: (10−4) = 6; [20−6] = 14; {40−14} = 26
Answer: 90 − 26 = 64 - 80 − [30 − {20 − (9 − 3)}]
Inside: (9−3) = 6; {20−6} = 14; [30−14] = 16
Answer: 80 − 16 = 64 - 100 − {45 − [25 − (12 − 6)]}
Inside: (12−6) = 6; [25−6] = 19; {45−19} = 26
Answer: 100 − 26 = 74 - 120 − [60 − {30 − (18 − 9)}]
Inside: (18−9) = 9; {30−9} = 21; [60−21] = 39
Answer: 120 − 39 = 81 - 85 − {35 − [20 − (9 − 4)]}
Inside: (9−4) = 5; [20−5] = 15; {35−15} = 20
Answer: 85 − 20 = 65 - 70 − [30 − {18 − (8 − 3)}]
Inside: (8−3) = 5; {18−5} = 13; [30−13] = 17
Answer: 70 − 17 = 53 - 95 − {50 − [28 − (15 − 7)]}
Inside: (15−7) = 8; [28−8] = 20; {50−20} = 30
Answer: 95 − 30 = 65 - 100 − [45 − {22 − (11 − 4)}]
Inside: (11−4) = 7; {22−7} = 15; [45−15] = 30
Answer: 100 − 30 = 70 - 88 − {44 − [24 − (10 − 3)]}
Inside: (10−3) = 7; [24−7] = 17; {44−17} = 27
Answer: 88 − 27 = 61 - 110 − [55 − {30 − (16 − 6)}]
Inside: (16−6) = 10; {30−10} = 20; [55−20] = 35
Answer: 110 − 35 = 75 - 75 − {35 − [20 − (9 − 2)]}
Inside: (9−2) = 7; [20−7] = 13; {35−13} = 22
Answer: 75 − 22 = 53 - 100 − [60 − {40 − (18 − 8)}]
Inside: (18−8) = 10; {40−10} = 30; [60−30] = 30
Answer: 100 − 30 = 70 - 90 − {45 − [30 − (17 − 9)]}
Inside: (17−9) = 8; [30−8] = 22; {45−22} = 23
Answer: 90 − 23 = 67 - 80 − [40 − {25 − (14 − 6)}]
Inside: (14−6) = 8; {25−8} = 17; [40−17] = 23
Answer: 80 − 23 = 57 - 120 − {70 − [40 − (20 − 5)]}
Inside: (20−5) = 15; [40−15] = 25; {70−25} = 45
Answer: 120 − 45 = 75 - 65 − [30 − {18 − (12 − 7)}]
Inside: (12−7) = 5; {18−5} = 13; [30−13] = 17
Answer: 65 − 17 = 48 - 95 − {55 − [35 − (20 − 8)]}
Inside: (20−8) = 12; [35−12] = 23; {55−23} = 32
Answer: 95 − 32 = 63 - 100 − [50 − {30 − (16 − 10)}]
Inside: (16−10) = 6; {30−6} = 24; [50−24] = 26
Answer: 100 − 26 = 74 - 88 − {44 − [28 − (12 − 6)]}
Inside: (12−6) = 6; [28−6] = 22; {44−22} = 22
Answer: 88 − 22 = 66 - 70 − [35 − {20 − (11 − 5)}]
Inside: (11−5) = 6; {20−6} = 14; [35−14] = 21
Answer: 70 − 21 = 49 - 105 − {60 − [35 − (20 − 8)]}
Inside: (20−8) = 12; [35−12] = 23; {60−23} = 37
Answer: 105 − 37 = 68 - 90 − [45 − {25 − (15 − 10)}]
Inside: (15−10) = 5; {25−5} = 20; [45−20] = 25
Answer: 90 − 25 = 65 - 100 − {50 − [30 − (18 − 12)]}
Inside: (18−12) = 6; [30−6] = 24; {50−24} = 26
Answer: 100 − 26 = 74 - 80 − [40 − {25 − (14 − 8)}]
Inside: (14−8) = 6; {25−6} = 19; [40−19] = 21
Answer: 80 − 21 = 59 - 95 − {50 − [30 − (17 − 11)]}
Inside: (17−11) = 6; [30−6] = 24; {50−24} = 26
Answer: 95 − 26 = 69
Category 4: Expressions with Fractions and Decimals
(Problems incorporating fractions, percentages, and decimals)
- 3.5 + 2.4 − 1.7
Answer: 4.2 - ½ × ¾ − ¼ + ¼
Calculation: ½×¾ = 3/8; then (–¼ + ¼ = 0)
Answer: 3/8 - ¾% of 280 − ¼% of 800
Interpret as percentages: 0.75% of 280 = 280×0.0075 = 2.1; 0.25% of 800 = 800×0.0025 = 2.0
Answer: 0.1 - 0.5 + 0.25 − 0.1
Answer: 0.65 - ⅓ + ⅙
Common denominator: 2/6 + 1/6 = 3/6
Answer: ½ - (2/5) × 10
Answer: 4 - 0.75 − 0.5 + 0.2
Answer: 0.45 - 1.2 + 2.8 − 1.5
Answer: 2.5 - 3/8 + 1/8
Answer: 1/2 - 5/10 + 3/10
Answer: 8/10 or 4/5 - 1.1 − 0.4 + 0.3
Answer: 1.0 - (2/3) − (1/6)
Common denominator: 4/6 − 1/6 = 3/6
Answer: ½ - 0.2 × 5
Answer: 1.0 - 0.6 ÷ 0.2
Answer: 3 - 3.5 − ½
(½ = 0.5)
Answer: 3.0 - ¼ + 0.25
(¼ = 0.25)
Answer: 0.5 - 0.5 × 0.5
Answer: 0.25 - 2.4 − 1.2
Answer: 1.2 - 0.75 + 0.75
Answer: 1.5 - ½ ÷ ¼
Answer: 2 - 3/5 + 2/5
Answer: 1 - 0.9 − 0.3
Answer: 0.6 - 2.5 + 1.5
Answer: 4.0 - (3/10) × 10
Answer: 3 - ½ + ⅓
Common denominator: 3/6 + 2/6 = 5/6
Answer: 5/6 - 0.4 + 0.6
Answer: 1.0 - 2.2 − 0.2
Answer: 2.0 - 1.5 + 2.5
Answer: 4.0 - ¾ − ½
Convert to common denominator: 3/4 − 2/4 = 1/4
Answer: ¼ - 0.8 ÷ 0.4
Answer: 2 - 1.2 + 3.3
Answer: 4.5 - 2.5 − 1.1
Answer: 1.4 - (3/8) × 8
Answer: 3 - 0.33 + 0.67
Answer: 1.0 - 5/6 − ⅓
Common denominator: 5/6 − 2/6 = 3/6
Answer: ½ - ½ + ⅔
Common denominator: 3/6 + 4/6 = 7/6
Answer: 7/6 - 2.5 × 2
Answer: 5.0 - ¼ ÷ ½
Answer: ½ - 0.2 + 0.3
Answer: 0.5 - 0.7 − 0.4
Answer: 0.3 - 3.6 + 1.4
Answer: 5.0 - 0.9 × 2
Answer: 1.8 - 1.5 − 0.5
Answer: 1.0 - (2/5) + (3/5)
Answer: 1 - 0.4 ÷ 0.2
Answer: 2 - (1/8) + (3/8)
Answer: ½ - 0.25 × 4
Answer: 1 - 1.2 ÷ 0.4
Answer: 3 - 2.5 − 0.5
Answer: 2.0 - ¾ + ¼
Answer: 1
Category 5: Word Problems
(Translate worded descriptions into mathematical expressions and then solve)
- “Nine multiplied by the sum of two and five.”
Expression: 9 × (2 + 5)
Answer: 63 - “Twelve divided by the sum of one and three.”
Expression: 12 ÷ (1 + 3)
Answer: 3 - “Twenty divided by the difference of seven and two.”
Expression: 20 ÷ (7 − 2)
Answer: 4 - “Eight plus the product of three and four.”
Expression: 8 + (3 × 4)
Answer: 20 - “Fifteen minus the sum of five and three.”
Expression: 15 − (5 + 3)
Answer: 7 - “The product of six and the difference of ten and four.”
Expression: 6 × (10 − 4)
Answer: 36 - “Twenty-five divided by the sum of five and five.”
Expression: 25 ÷ (5 + 5)
Answer: 2.5 - “Thirty plus the quotient of forty and eight.”
Expression: 30 + (40 ÷ 8)
Answer: 35 - “Fifty minus the product of two and ten.”
Expression: 50 − (2 × 10)
Answer: 30 - “Eighty divided by the sum of four and six.”
Expression: 80 ÷ (4 + 6)
Answer: 8 - “The sum of twelve and eight multiplied by two.”
Expression: (12 + 8) × 2
Answer: 40 - “Thirty-six divided by the difference of nine and three.”
Expression: 36 ÷ (9 − 3)
Answer: 6 - “Twenty multiplied by the difference of fifteen and five.”
Expression: 20 × (15 − 5)
Answer: 200 - “Forty plus the product of three and seven.”
Expression: 40 + (3 × 7)
Answer: 61 - “Sixty minus the sum of twenty and ten.”
Expression: 60 − (20 + 10)
Answer: 30 - “The product of four and the sum of five and six.”
Expression: 4 × (5 + 6)
Answer: 44 - “Eighty divided by the difference of ten and two.”
Expression: 80 ÷ (10 − 2)
Answer: 10 - “Twenty-five plus the quotient of fifty and ten.”
Expression: 25 + (50 ÷ 10)
Answer: 30 - “Thirty minus the product of two and nine.”
Expression: 30 − (2 × 9)
Answer: 12 - “The sum of fifteen and twenty multiplied by three.”
Expression: (15 + 20) × 3
Answer: 105 - “Fifty divided by the sum of five and five.”
Expression: 50 ÷ (5 + 5)
Answer: 5 - “Ninety minus the product of three and ten.”
Expression: 90 − (3 × 10)
Answer: 60 - “Thirty multiplied by the sum of two and three.”
Expression: 30 × (2 + 3)
Answer: 150 - “Sixty divided by the difference of eight and two.”
Expression: 60 ÷ (8 − 2)
Answer: 10 - “Twenty plus the product of four and five.”
Expression: 20 + (4 × 5)
Answer: 40 - “The sum of thirty and twenty divided by five.”
Expression: (30 + 20) ÷ 5
Answer: 10 - “Forty minus the quotient of twenty and two.”
Expression: 40 − (20 ÷ 2)
Answer: 30 - “Eighty plus the product of two and fifteen.”
Expression: 80 + (2 × 15)
Answer: 110 - “Fifty divided by the difference of seven and two.”
Expression: 50 ÷ (7 − 2)
Answer: 10 - “The product of nine and the sum of three and four.”
Expression: 9 × (3 + 4)
Answer: 63 - “Thirty-five plus the quotient of sixty and twelve.”
Expression: 35 + (60 ÷ 12)
Answer: 40 - “Twenty-four divided by the difference of six and two.”
Expression: 24 ÷ (6 − 2)
Answer: 6 - “Fifty minus the sum of ten and fifteen.”
Expression: 50 − (10 + 15)
Answer: 25 - “The product of eight and the difference of nine and three.”
Expression: 8 × (9 − 3)
Answer: 48 - “Sixty plus the quotient of seventy-two and eight.”
Expression: 60 + (72 ÷ 8)
Answer: 69 - “Twenty divided by the sum of four and one.”
Expression: 20 ÷ (4 + 1)
Answer: 4 - “The sum of fifty and thirty multiplied by two.”
Expression: (50 + 30) × 2
Answer: 160 - “Ninety minus the product of five and eight.”
Expression: 90 − (5 × 8)
Answer: 50 - “Forty divided by the difference of six and two.”
Expression: 40 ÷ (6 − 2)
Answer: 10 - “Thirty plus the product of seven and three.”
Expression: 30 + (7 × 3)
Answer: 51 - “The quotient of eighty and four plus six.”
Expression: (80 ÷ 4) + 6
Answer: 26 - “Fifty minus the difference of twenty and ten.”
Expression: 50 − (20 − 10)
Answer: 40 - “The product of six and the sum of seven and eight.”
Expression: 6 × (7 + 8)
Answer: 90 - “Eighty divided by the sum of eight and two.”
Expression: 80 ÷ (8 + 2)
Answer: 8 - “Thirty-five plus the product of four and six.”
Expression: 35 + (4 × 6)
Answer: 59 - “The difference of seventy and the product of five and six.”
Expression: 70 − (5 × 6)
Answer: 40 - “Forty divided by the sum of three and two.”
Expression: 40 ÷ (3 + 2)
Answer: 8 - “The sum of twenty and ten multiplied by four.”
Expression: (20 + 10) × 4
Answer: 120 - “Fifty minus the quotient of thirty and two.”
Expression: 50 − (30 ÷ 2)
Answer: 35 - “The product of seven and the difference of nine and two.”
Expression: 7 × (9 − 2)
Answer: 49
These 250 questions (50 per category) provide a wide variety of practice opportunities—ranging from basic operations through multi-level bracket problems and word-problem translations. Use them to build your confidence with order of operations, fractions/decimals, and converting words into expressions.
You can fine the questionnaire for practice here.
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