krit.club logo

Fractions, Decimals, and Percentages - Converting improper fractions to mixed numbers

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number).

•

A mixed number consists of a whole number and a proper fraction combined.

•

Converting an improper fraction to a mixed number involves division: the quotient becomes the whole number, and the remainder becomes the new numerator.

•

The denominator remains the same during the conversion process.

📐Formulae

Improper Fraction=NumeratorDenominator\text{Improper Fraction} = \frac{\text{Numerator}}{\text{Denominator}}

Mixed Number=QuotientRemainderDenominator\text{Mixed Number} = \text{Quotient} \frac{\text{Remainder}}{\text{Denominator}}

Numerator÷Denominator=Quotient with a Remainder\text{Numerator} \div \text{Denominator} = \text{Quotient with a Remainder}

💡Examples

Problem 1:

Convert 134\frac{13}{4} into a mixed number.

Solution:

3143 \frac{1}{4}

Explanation:

Divide the numerator (13) by the denominator (4). 13÷4=313 \div 4 = 3 with a remainder of 11. The quotient (3) becomes the whole number, the remainder (1) becomes the numerator, and the denominator (4) stays the same.

Problem 2:

Convert 225\frac{22}{5} into a mixed number.

Solution:

4254 \frac{2}{5}

Explanation:

Divide 22 by 5. 5 goes into 22 four times (5×4=205 \times 4 = 20), leaving a remainder of 22 (22−20=222 - 20 = 2). Thus, the mixed number is 44 wholes and 22 fifths.

Problem 3:

Convert 173\frac{17}{3} into a mixed number.

Solution:

5235 \frac{2}{3}

Explanation:

Perform the division: 17÷317 \div 3. Since 3×5=153 \times 5 = 15, the quotient is 5. The remainder is 17−15=217 - 15 = 2. Place the remainder over the original denominator to get 5235 \frac{2}{3}.