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Calculate the following: a) 16 / 4 + 2 b) 17 - 2 x (5 - 3) c) 10 + 3 - 2 d) 9 - 4 + 6. Find the value of: a) 12 - 4 x 2 b) 15 + 8 - 4 x 2 c) 7 x (5 + 3) - 12 / 4 d) 9 + 6 x (8 - 4) / 2 e) 50 / 5 + 4 x

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  1. Calculate

    • a) 16÷4+216 \div 4 + 2 16÷4+2=4+2=616 \div 4 + 2 = 4 + 2 = \boxed{\text{6}}
    • b) 17−2×(5−3)17 - 2 \times (5 - 3) 17−2×(5−3)=17−2×2=17−4=1317 - 2 \times (5 - 3) = 17 - 2 \times 2 = 17 - 4 = \boxed{\text{13}}
    • c) 10+3−210 + 3 - 2 10+3−2=13−2=1110 + 3 - 2 = 13 - 2 = \boxed{\text{11}}
    • d) 9−4+69 - 4 + 6 9−4+6=5+6=119 - 4 + 6 = 5 + 6 = \boxed{\text{11}}

  2. Find the value of

    • a) 12−4×212 - 4 \times 2 12−4×2=12−8=412 - 4 \times 2 = 12 - 8 = \boxed{\text{4}}
    • b) 15+8−4×215 + 8 - 4 \times 2 15+8−4×2=15+8−8=23−8=1515 + 8 - 4 \times 2 = 15 + 8 - 8 = 23 - 8 = \boxed{\text{15}}
    • c) 7×(5+3)−12÷47 \times (5 + 3) - 12 \div 4 7×(5+3)−12÷4=7×8−12÷4=56−3=537 \times (5 + 3) - 12 \div 4 = 7 \times 8 - 12 \div 4 = 56 - 3 = \boxed{\text{53}}
    • d) 9+6×(8−4)÷29 + 6 \times (8 - 4) \div 2 9+6×(8−4)÷2=9+6×4÷2=9+24÷2=9+12=219 + 6 \times (8 - 4) \div 2 = 9 + 6 \times 4 \div 2 = 9 + 24 \div 2 = 9 + 12 = \boxed{\text{21}}
    • e) 50÷5+4×7−350 \div 5 + 4 \times 7 - 3 50÷5+4×7−3=10+28−3=38−3=3550 \div 5 + 4 \times 7 - 3 = 10 + 28 - 3 = 38 - 3 = \boxed{\text{35}}

  3. Convert EACH of the following to an improper fraction

    • a) 83208 \frac{3}{20} 8320=8×20+320=160+320=163208 \frac{3}{20} = \frac{8 \times 20 + 3}{20} = \frac{160 + 3}{20} = \boxed{\frac{163}{20}}
    • b) 1059010 \frac{5}{90} 10590=10×90+590=900+590=9059010 \frac{5}{90} = \frac{10 \times 90 + 5}{90} = \frac{900 + 5}{90} = \frac{905}{90} Simplify by dividing numerator and denominator by 5: 905÷590÷5=18118\frac{905 \div 5}{90 \div 5} = \boxed{\frac{181}{18}}
    • c) 1451 \frac{4}{5} 145=1×5+45=5+45=951 \frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{5 + 4}{5} = \boxed{\frac{9}{5}}

  4. Convert EACH of the following to a mixed number

    • a) 387\frac{38}{7} Divide 38 by 7: 38÷7=538 \div 7 = 5 with a remainder of 3. 387=537\frac{38}{7} = \boxed{5 \frac{3}{7}}
    • b) 154\frac{15}{4} Divide 15 by 4: 15÷4=315 \div 4 = 3 with a remainder of 3. 154=334\frac{15}{4} = \boxed{3 \frac{3}{4}}
    • c) 9610\frac{96}{10} Divide 96 by 10: 96÷10=996 \div 10 = 9 with a remainder of 6. 9610=9610\frac{96}{10} = 9 \frac{6}{10} Simplify the fraction part: 96÷210÷2=9359 \frac{6 \div 2}{10 \div 2} = \boxed{9 \frac{3}{5}}

  5. Simplify EACH of the following

    • a) 56+34\frac{5}{6} + \frac{3}{4} Find a common denominator (LCM of 6 and 4 is 12): 56+34=5×26×2+3×34×3=1012+912=10+912=1912\frac{5}{6} + \frac{3}{4} = \frac{5 \times 2}{6 \times 2} + \frac{3 \times 3}{4 \times 3} = \frac{10}{12} + \frac{9}{12} = \frac{10 + 9}{12} = \frac{19}{12} Convert to a mixed number: 1912=1712\frac{19}{12} = \boxed{1 \frac{7}{12}}
    • b) 212−1142 \frac{1}{2} - 1 \frac{1}{4} Convert mixed numbers to improper fractions: 212=2×2+12=522 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2} 114=1×4+14=541 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4} Subtract the improper fractions (common denominator is 4): 52−54=5×22×2−54=104−54=10−54=54\frac{5}{2} - \frac{5}{4} = \frac{5 \times 2}{2 \times 2} - \frac{5}{4} = \frac{10}{4} - \frac{5}{4} = \frac{10 - 5}{4} = \frac{5}{4} Convert to a mixed number: 54=114\frac{5}{4} = \boxed{1 \frac{1}{4}}
    • c) 45×38\frac{4}{5} \times \frac{3}{8} Multiply the numerators and the denominators: 45×38=4×35×8=1240\frac{4}{5} \times \frac{3}{8} = \frac{4 \times 3}{5 \times 8} = \frac{12}{40} Simplify by dividing numerator and denominator by 4: 12÷440÷4=310\frac{12 \div 4}{40 \div 4} = \boxed{\frac{3}{10}}
    • d) 57÷12\frac{5}{7} \div \frac{1}{2} Multiply the first fraction by the reciprocal of the second fraction: 57÷12=57×21=5×27×1=107\frac{5}{7} \div \frac{1}{2} = \frac{5}{7} \times \frac{2}{1} = \frac{5 \times 2}{7 \times 1} = \frac{10}{7} Convert to a mixed number: 107=137\frac{10}{7} = \boxed{1 \frac{3}{7}}
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