Basic operations with numbers

Given two numbers, say 88 and 44, we can apply four different operations to get a new number. They are called arithmetic operations:

addition: 8+4 (8 plus 4, or the sum of 8 and 4)subtraction: 8−4 (8 minus 4)multiplication: 8⋅4 (8 times 4, or the product of 8 and 4)division: 8:4 (8 divided by 4)\begin{array}{ll} \text{addition: } & 8+4 \quad\text{ (8 plus 4, or the sum of 8 and 4)}\\ \text{subtraction: } &8-4 \quad\text{ (8 minus 4)}\\ \text{multiplication: } & 8\cdot 4 \quad\text{ (8 times 4, or the product of 8 and 4)}\\ \text{division: } &8:4 \quad\text{ (8 divided by 4)}\\ \end{array}

But you already know that. Here are a few exercises about the basic operations. They can be solved without a calculator.

Exercise 1

Find for each picture below a corresponding calculation.

Solution
  1. 5+35+3
  2. 78−18\frac{7}{8}-\frac{1}{8}
  3. 14+18\frac{1}{4}+\frac{1}{8}
  4. 10−410-4
  5. 0+5−30+5-3
  6. 0+2−30+2-3
  7. 0−2+40-2+4
  8. 2+2+2+2+2=5⋅22+2+2+2+2=5\cdot 2
  9. 14+14+14=3⋅14\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=3\cdot \frac{1}{4}
Exercise 2
  1. The expression 4⋅74\cdot 7 is actually an abbreviation. What does it stand for?
  2. Addition and subtraction
    1. 2+8=2+8=
    2. 8−3=8-3=
    3. 8−11=8-11=
    4. −3−2=-3-2=
    5. 2+0=2+0=
    6. 0−5=0-5=
    7. 3−3=3-3=
    8. −5+5=-5+5=
    9. 10−4+5−7=10-4+5-7=
    10. 9438−2319=9438-2319=
  3. Multiplication
    1. 1⋅4=1\cdot 4=
    2. 6⋅1=6\cdot 1=
    3. 3⋅0=3\cdot 0=
    4. 0⋅2=0\cdot 2=
    5. 2⋅4=2\cdot 4=
    6. (2)(3)=(2)(3)=
    7. 6⋅(−5)=6\cdot (-5)=
    8. (−3)⋅8=(-3)\cdot 8=
    9. −1⋅3=-1\cdot 3=
    10. (−6)⋅(−2)=(-6)\cdot (-2)=
    11. 2⋅5⋅4=2\cdot 5\cdot 4 =
    12. 2⋅(4⋅5)=2\cdot (4\cdot 5)=
    13. (2⋅4)⋅5=(2\cdot 4)\cdot 5=
    14. 2⋅3⋅4⋅5⋅6=2\cdot 3\cdot 4\cdot 5\cdot 6=
  4. Addition and multiplication
    1. 3⋅(4+5)=3\cdot (4+5)=
    2. 3(4+5)=3(4+5)=
    3. −3(4+5)=-3(4+5)=
    4. 4+4⋅5=4+4\cdot 5=
    5. 5⋅6−4=5\cdot 6-4=
    6. 3⋅5+4⋅2=3\cdot 5 + 4\cdot 2=
    7. (3+5)(4−5)=(3+5)(4-5)=
  5. Division
    1. 6:3=6:3=
    2. −10:2=-10:2=
    3. 15:(−3)=15:(-3)=
    4. 3:6=3:6=
  6. Fractions

    1. 12+23=\frac{1}{2}+\frac{2}{3}=

    2. 34−18=\frac{3}{4}-\frac{1}{8}=

    3. 25−12=\frac{2}{5}-\frac{1}{2}=

    4. 2+13=2+\frac{1}{3}=

    5. 3−37=3-\frac{3}{7}=

    6. 32+1=\frac{3}{2}+1=

    7. 12+23−34=\frac{1}{2}+\frac{2}{3}-\frac{3}{4}=

    8. 12⋅37=\frac{1}{2}\cdot \frac{3}{7}=

    9. −23⋅45=\frac{-2}{3}\cdot\frac{4}{5}=

    10. 329=3\frac{2}{9}=

    11. 15⋅5=\frac{1}{5}\cdot 5=

    12. 13⋅31=\frac{1}{3}\cdot\frac{3}{1}=

    13. 23(12+14)=\frac{2}{3} \left( \frac{1}{2}+\frac{1}{4} \right)=

Solution
  1. 4⋅7=7+7+7+74\cdot 7=7+7+7+7
  2. Addition and subtraction
    1. 2+8=102+8=10
    2. 8−3=58-3=5
    3. 8−11=−38-11=-3
    4. −3−2=−5-3-2=-5
    5. 2+0=22+0=2
    6. 0−5=−50-5=-5
    7. 3−3=03-3=0
    8. −5+5=0-5+5=0
    9. 10−4+5−7=410-4+5-7=4
    10. 9438−2319=71199438-2319=7119
  3. Multiplication
    1. 1⋅4=41\cdot 4=4
    2. 6⋅1=66\cdot 1=6
    3. 3⋅0=03\cdot 0=0
    4. 0⋅2=00\cdot 2=0
    5. 2⋅4=82\cdot 4=8
    6. (2)(3)=6(2)(3)=6
    7. 6⋅(−5)=−306\cdot (-5)=-30
    8. (−3)⋅8=−24(-3)\cdot 8=-24
    9. −1⋅3=−3-1\cdot 3=-3
    10. (−6)⋅(−2)=12(-6)\cdot (-2)=12
    11. 2⋅5⋅4=402\cdot 5\cdot 4 =40
    12. 2⋅(4⋅5)=402\cdot (4\cdot 5)=40
    13. (2⋅4)⋅5=40(2\cdot 4)\cdot 5=40
    14. 2⋅3⋅4⋅5⋅6=7202\cdot 3\cdot 4\cdot 5\cdot 6=720
  4. Addition and multiplication
    1. 3⋅(4+5)=273\cdot (4+5)=27
    2. 3(4+5)=273(4+5)=27
    3. −3(4+5)=−27-3(4+5)=-27
    4. 4+4⋅5=244+4\cdot 5=24
    5. 5⋅6−4=265\cdot 6-4=26
    6. 3⋅5+4⋅2=233\cdot 5 + 4\cdot 2=23
    7. (3+5)(4−5)=8⋅(−1)=−8(3+5)(4-5)=8\cdot(-1)=-8
  5. Division
    1. 6:3=26:3=2
    2. −10:2=−5-10:2=-5
    3. 15:(−3)=−515:(-3)=-5
    4. 3:6=0.53:6=0.5
  6. Fractions
    1. 12+23=36+46=76\frac{1}{2}+\frac{2}{3}=\frac{3}{6}+\frac{4}{6}=\frac{7}{6}
    2. 34−18=68−18=58\frac{3}{4}-\frac{1}{8}=\frac{6}{8}-\frac{1}{8}=\frac{5}{8}
    3. 25−12=410−510=−110=−110\frac{2}{5}-\frac{1}{2}=\frac{4}{10}-\frac{5}{10}=\frac{-1}{10}=-\frac{1}{10}
    4. 2+13=21+13=63+13=732+\frac{1}{3}=\frac{2}{1}+\frac{1}{3}=\frac{6}{3}+\frac{1}{3}=\frac{7}{3}
    5. 3−37=31−37=217−37=1873-\frac{3}{7}=\frac{3}{1}-\frac{3}{7}=\frac{21}{7}-\frac{3}{7}=\frac{18}{7}
    6. 32+1=32+21=32+22=52\frac{3}{2}+1=\frac{3}{2}+\frac{2}{1}=\frac{3}{2}+\frac{2}{2}=\frac{5}{2}
    7. 12+23−34=612+812−912=512\frac{1}{2}+\frac{2}{3}-\frac{3}{4}=\frac{6}{12}+\frac{8}{12}-\frac{9}{12}=\frac{5}{12}
    8. 12⋅37=1⋅32⋅7=314\frac{1}{2}\cdot \frac{3}{7}=\frac{1\cdot 3}{2\cdot 7}=\frac{3}{14}
    9. −23⋅45=−2⋅43⋅5=−815=−815\frac{-2}{3}\cdot\frac{4}{5}=\frac{-2\cdot 4}{3\cdot 5}=\frac{-8}{15}=-\frac{8}{15}
    10. 329=31⋅29=69=233\frac{2}{9}=\frac{3}{1}\cdot \frac{2}{9}=\frac{6}{9}=\frac{2}{3}
    11. 15⋅5=15⋅51=55=1\frac{1}{5}\cdot 5=\frac{1}{5}\cdot\frac{5}{1}=\frac{5}{5}=1
    12. 13⋅31=33=1\frac{1}{3}\cdot\frac{3}{1}=\frac{3}{3}=1
    13. 23(12+14)=23⋅34=612=12\frac{2}{3} \left( \frac{1}{2}+\frac{1}{4} \right)=\frac{2}{3}\cdot \frac{3}{4}=\frac{6}{12}=\frac{1}{2}