krit.club logo

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

Grade 4IGCSE

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). It represents a value greater than or equal to 1.

•

A mixed number is a way of expressing an improper fraction using a whole number and a proper fraction combined.

•

The process of conversion is based on division: the fraction bar acts as a division symbol.

•

The denominator always stays the same when converting between improper fractions and mixed numbers.

📐Formulae

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

Whole Number=Numerator÷Denominator (Quotient)\text{Whole Number} = \text{Numerator} \div \text{Denominator} \text{ (Quotient)}

New Numerator=Remainder of the division\text{New Numerator} = \text{Remainder of the division}

Mixed Number=Whole NumberRemainderDenominator\text{Mixed Number} = \text{Whole Number} \frac{\text{Remainder}}{\text{Denominator}}

💡Examples

Problem 1:

Convert 114\frac{11}{4} to a mixed number.

Solution:

2342 \frac{3}{4}

Explanation:

Divide 11 by 4. 11÷4=211 \div 4 = 2 with a remainder of 33. The quotient '2' becomes the whole number. The remainder '3' becomes the numerator. The denominator '4' stays the same.

Problem 2:

Convert 175\frac{17}{5} to a mixed number.

Solution:

3253 \frac{2}{5}

Explanation:

Divide 17 by 5. 55 goes into 1717 three times (5×3=155 \times 3 = 15). The remainder is 17−15=217 - 15 = 2. Therefore, we have 3 wholes and 2 fifths left over.

Problem 3:

Express 92\frac{9}{2} as a mixed number.

Solution:

4124 \frac{1}{2}

Explanation:

Divide 9 by 2. 9÷2=49 \div 2 = 4 remainder 11. This results in the mixed number 4124 \frac{1}{2}.