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Improper Fractions Practice

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Improper Fractions Practice

Levi and Keira are checking fraction labels for materials at a hardware store. Convert between improper fractions and mixed numbers. Show your working where asked. Simplify fractions when possible.

Build the whole number

To change an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number; the remainder becomes the new numerator, with the same denominator. For example, 11/4 = 2 3/4 because 11 = 2 × 4 + 3.

1.Hugo finds a roll label showing 17/5 metres. Convert 17/5 to a mixed number. Show the division or an equivalent equation.

2.A box of bolts is labelled 23/6 kg. Write this improper fraction as a mixed number in simplest form.

3.Keira writes 19/4 = 4 3/4. Is she correct? Choose an answer and explain how you checked.

Yes; 19 ÷ 4 is 4 remainder 3.
No; 19 ÷ 4 is 3 remainder 7.
No; the denominator should be 3.
Yes; 19 ÷ 4 is 4 remainder 4.

4.Levi measures a piece of timber as 14/3 m. Complete the equivalent mixed number: 14/3 = /3. Show how many whole groups of thirds there are.

Rebuild the fraction

To change a mixed number to an improper fraction, multiply the whole number by the denominator, then add the numerator. Keep the denominator the same.

5.A shelf bracket needs a timber strip 2 3/8 m long. Convert 2 3/8 to an improper fraction. Write the multiplication and addition you used.

6.Convert 5 2/7 to an improper fraction. Include one equation to show your method.

7.A paint tin label says 3 4/9 L. What is this as an improper fraction?

Check the stock labels

Use the conversion in each question to decide whether a label is equivalent. Fractions should be simplified if possible. For the ordering question, convert each amount to a common form or compare its value, then order the amounts from least to greatest.

8.True or false: 2 5/6 is equal to 17/6. If false, write the correct improper fraction.

TrueFalse

9.A price card has been smudged: 4 1/5 = /5. Find the missing numerator and explain briefly.

10.Put these amounts in order from least to greatest: 11/4 m, 2 2/3 m, and 17/6 m. Convert them to a common form or compare their values to justify your order.

11.The store receives 3 3/4 m of cable. Hugo says that is 15/4 m, while Levi says it is 12/4 m. Who is correct? Show a calculation and explain the other answer’s mistake.