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Fractions

1.0 Numbers · 1.4 Fractions

Syllabus tag: Kenya CBC | Grade 6 Mathematics | Strand 1.0 Numbers | Sub-Strand 1.4 Fractions (12 Lessons)

Lesson objectives

By the end of this topic, you will be able to:

  • Add and subtract fractions using LCM
  • Add and subtract mixed numbers
  • Identify the reciprocal of a proper fraction
  • Work out squares of fractions
  • Express a fraction as a percentage, and convert a percentage to a fraction
  • Appreciate the use of fractions in real life

Fractions

A fraction shows part of a whole. The bottom says how many equal parts there are. The top says how many are taken.

a) Adding and subtracting

Fractions can only be added when their bottoms are the same.

Adding with the LCM Adding with the LCM 2/3 + 1/4 = ? different bottoms LCM of 3 and 4 = 12 the common bottom 2/3 + 1/4 = 8/12 + 3/12 rewrite both 2/3 + 1/4 = 11/12 add the tops only

Find the LCM of the two bottoms. That becomes the common bottom.

Rewrite each fraction with it, then add or subtract the tops only.

The bottom never changes when adding. 1/2 + 1/2 is 1, not 2/4.

b) Mixed numbers

A mixed number has a whole part and a fraction part, such as 2¼.

Adding mixed numbers Adding mixed numbers 2¼ + 1½ = ? whole parts and fraction parts the wholes → 2 + 1 = 3 add them first the fractions → 1/4 + 2/4 = 3/4 same bottom now 2¼ + 1½ = 3¾ put them together

Add the whole parts, then add the fraction parts, then put them together.

If the fraction part comes to more than 1, carry the extra into the whole part. So 3 + 5/4 becomes 4¼.

In subtraction the first fraction part may be too small. Borrow 1 from the whole part and turn it into a fraction.

c) The reciprocal

The reciprocal of a fraction is that fraction turned upside down.

The reciprocal of 3/5 is 5/3. The reciprocal of 2/7 is 7/2.

A fraction times its own reciprocal always gives 1.

d) Squares of fractions

To square a fraction, square the top and square the bottom.

So (3/5)² is 9/25, because 3 × 3 = 9 and 5 × 5 = 25.

e) Fractions and percentages

Per cent means "out of 100".

Fractions and percentages Fractions and percentages 3/4 becomes = 3/4 × 100 multiply by 100 3/4 becomes = 75% as a percentage 40% becomes = 40/100 percent means out of 100 40% becomes = 2/5 simplified

To turn a fraction into a percentage, multiply by 100.

To turn a percentage into a fraction, write it over 100 and simplify.

Some are worth learning by heart. ½ is 50%, ¼ is 25%, ¾ is 75%, and ⅕ is 20%.

f) Where this is used

Sharing food equally. Reading a discount in a shop. Measuring in a recipe. Understanding a test score written as a percentage.

Words to know

  • LCM (Lowest Common Multiple) — the smallest number that two or more denominators divide into exactly.
  • Mixed number — a whole number and a fraction together, like 2 1/3.
  • Reciprocal — the fraction you get by swapping the numerator and denominator; a fraction multiplied by its reciprocal equals 1.
  • Percentage — a fraction expressed out of 100, shown with the % sign.

:::checkpoint Check yourself

  1. Work out 1/2 + 1/3.
  2. Work out 3½ + 2¼.
  3. Write 2/5 as a percentage.
  4. Write 60% as a fraction in its simplest form. :::

Bridge to practice

Try the exercises below — LCM addition and subtraction, mixed numbers, reciprocals, squares, and fraction-percentage conversions, the same skills covered above.

Check yourselfPractise Fractions — 10 questions →Next in MathematicsDecimals →