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Solve the following problems: 1. If 560 oranges are divided equally among 70 pupils, how many oranges does each pupil get? 2. How many times does 14 go into 30500? 3. Convert the following mixed numbe

Mathematics

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Answers

5 parts
a

54\frac{5}{4}

b

52\frac{5}{2}

c

113\frac{11}{3}

d

457\frac{45}{7}

e

727\frac{72}{7}

Step-by-step solution

11 steps

Here are the solutions to your homework questions:

1.

Step 1: Divide the total number of oranges by the number of pupils.

Oranges per pupil=560 oranges70 pupils\text{Oranges per pupil} = \frac{560 \text{ oranges}}{70 \text{ pupils}}

Step 2: Calculate the result.

Oranges per pupil=8\text{Oranges per pupil} = 8

Each pupil will have 8 oranges.

8 oranges\boxed{\text{8 oranges}}

2.

Step 1: Divide 30500 by 14 to find how many times 14 is contained in 30500.

3050014\frac{30500}{14}

Step 2: Perform the division and simplify the fraction.

3050014=152507\frac{30500}{14} = \frac{15250}{7}

Step 3: Convert the improper fraction to a mixed number.

152507=217847\frac{15250}{7} = 2178 \frac{4}{7}

14 is contained 2178 and 47\frac{4}{7} times in 30500.

217847\boxed{2178 \frac{4}{7}}

3. Changing them to improper fractions:

Part a· 2 steps

1141 \frac{1}{4}

  1. Multiply the whole number by the denominator and add the numerator.

    Keep the same denominator.

    114=(1×4)+141 \frac{1}{4} = \frac{(1 \times 4) + 1}{4}

  2. Simplify the numerator.

    4+14=54\frac{4 + 1}{4} = \frac{5}{4} 54\boxed{\frac{5}{4}}

Part b

52\frac{5}{2}

2362 \frac{3}{6}

  1. Multiply the whole number by the denominator and add the numerator.

    Keep the same denominator.

    236=(2×6)+362 \frac{3}{6} = \frac{(2 \times 6) + 3}{6}

  2. Simplify the numerator.

    12+36=156\frac{12 + 3}{6} = \frac{15}{6}

  3. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3.

    15÷36÷3=52\frac{15 \div 3}{6 \div 3} = \frac{5}{2} 52\boxed{\frac{5}{2}}

Part c

113\frac{11}{3}

3233 \frac{2}{3}

  1. Multiply the whole number by the denominator and add the numerator.

    Keep the same denominator.

    323=(3×3)+233 \frac{2}{3} = \frac{(3 \times 3) + 2}{3}

  2. Simplify the numerator.

    9+23=113\frac{9 + 2}{3} = \frac{11}{3} 113\boxed{\frac{11}{3}}

Part d

457\frac{45}{7}

6376 \frac{3}{7}

  1. Multiply the whole number by the denominator and add the numerator.

    Keep the same denominator.

    637=(6×7)+376 \frac{3}{7} = \frac{(6 \times 7) + 3}{7}

  2. Simplify the numerator.

    42+37=457\frac{42 + 3}{7} = \frac{45}{7} 457\boxed{\frac{45}{7}}

Part e

727\frac{72}{7}

102710 \frac{2}{7}

  1. Multiply the whole number by the denominator and add the numerator.

    Keep the same denominator.

    1027=(10×7)+2710 \frac{2}{7} = \frac{(10 \times 7) + 2}{7}

  2. Simplify the numerator.

    70+27=727\frac{70 + 2}{7} = \frac{72}{7} 727\boxed{\frac{72}{7}}
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