krit.club logo

Fractions, Decimals, and Percentages - Improper fractions and mixed numbers

Grade 6IGCSE

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.

•

To convert a mixed number to an improper fraction: Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.

•

To convert an improper fraction to a mixed number: Divide the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator remains the same.

•

Simplifying fractions is essential; always ensure the fractional part of a mixed number is in its simplest form.

📐Formulae

Mixed to Improper: Wnd=(W×d)+nd\text{Mixed to Improper: } W\frac{n}{d} = \frac{(W \times d) + n}{d}

Improper to Mixed: ND=QRD (where Q is quotient and R is remainder)\text{Improper to Mixed: } \frac{N}{D} = Q\frac{R}{D} \text{ (where } Q \text{ is quotient and } R \text{ is remainder)}

💡Examples

Problem 1:

Convert the mixed number 4374\frac{3}{7} into an improper fraction.

Solution:

317\frac{31}{7}

Explanation:

Multiply the whole number (4) by the denominator (7): 4×7=284 \times 7 = 28. Add the numerator (3): 28+3=3128 + 3 = 31. Place this over the original denominator to get 317\frac{31}{7}.

Problem 2:

Convert the improper fraction 175\frac{17}{5} into a mixed number.

Solution:

3253\frac{2}{5}

Explanation:

Divide 17 by 5. 17÷5=317 \div 5 = 3 with a remainder of 22. The quotient (3) is the whole number, the remainder (2) is the numerator, and the denominator (5) stays the same.

Problem 3:

Convert 224\frac{22}{4} to a mixed number and simplify the result.

Solution:

5125\frac{1}{2}

Explanation:

First, divide 22 by 4: 22÷4=522 \div 4 = 5 remainder 22. This gives 5245\frac{2}{4}. Since 2 and 4 are both divisible by 2, simplify the fraction 24\frac{2}{4} to 12\frac{1}{2}. The final simplified mixed number is 5125\frac{1}{2}.