What Are Lowest Terms?

Hello Year 4! Today, we’re going to learn about something called lowest terms. This is a way of simplifying fractions so they are as simple as possible.

What is a Fraction?

A fraction shows a part of a whole. For example, if you have a pizza cut into 4 equal slices and you eat 1 slice, you have eaten $$\frac{1}{4}$$ of the pizza.

What Does “Lowest Terms” Mean?

When we talk about lowest terms, we mean that the fraction is simplified. This means there are no numbers that can divide evenly into both the top number (the numerator) and the bottom number (the denominator) except for 1.

For example, the fraction $$\frac{4}{8}$$ is not in lowest terms because both 4 and 8 can be divided by 4. If we divide both the top and bottom by 4, we get $$\frac{1}{2}$$. Now, $$\frac{1}{2}$$ is in lowest terms!

How Do We Simplify Fractions?

  1. Find the Greatest Common Divisor (GCD): This is the biggest number that can divide both the numerator and the denominator.
  2. Divide both the top and bottom by the GCD.

Example

Let’s simplify the fraction $$\frac{6}{12}$$.

  1. Find the GCD: The GCD of 6 and 12 is 6.
  2. Divide both numbers:
    • Top: $$6 \div 6 = 1$$
    • Bottom: $$12 \div 6 = 2$$

So, $$\frac{6}{12}$$ in lowest terms is $$\frac{1}{2}$$.

Key Rules for Lowest Terms

  • Always look for the GCD.
  • Both the numerator and the denominator must be divided by the same number.
  • If the GCD is 1, the fraction is already in lowest terms!

Tips and Tricks

  • Remember: If both numbers can be divided by 2, you can simplify by 2.
  • You can also use a factor tree to find the GCD.
  • Practising with different fractions helps you get better at finding lowest terms!

Questions to Practice

Easy Level Questions

  1. Simplify $$\frac{2}{4}$$.
  2. Simplify $$\frac{3}{6}$$.
  3. Simplify $$\frac{5}{10}$$.
  4. Simplify $$\frac{8}{12}$$.
  5. Simplify $$\frac{1}{2}$$.
  6. Simplify $$\frac{4}{8}$$.
  7. Simplify $$\frac{9}{12}$$.
  8. Simplify $$\frac{10}{15}$$.
  9. Simplify $$\frac{6}{9}$$.
  10. Simplify $$\frac{18}{24}$$.

Medium Level Questions

  1. Simplify $$\frac{12}{16}$$.
  2. Simplify $$\frac{14}{21}$$.
  3. Simplify $$\frac{20}{25}$$.
  4. Simplify $$\frac{8}{20}$$.
  5. Simplify $$\frac{15}{30}$$.
  6. Simplify $$\frac{27}{36}$$.
  7. Simplify $$\frac{30}{45}$$.
  8. Simplify $$\frac{24}{32}$$.
  9. Simplify $$\frac{36}{48}$$.
  10. Simplify $$\frac{50}{100}$$.

Hard Level Questions

  1. Simplify $$\frac{45}{60}$$.
  2. Simplify $$\frac{56}{84}$$.
  3. Simplify $$\frac{63}{81}$$.
  4. Simplify $$\frac{80}{100}$$.
  5. Simplify $$\frac{72}{96}$$.
  6. Simplify $$\frac{54}{90}$$.
  7. Simplify $$\frac{99}{121}$$.
  8. Simplify $$\frac{88}{132}$$.
  9. Simplify $$\frac{100}{250}$$.
  10. Simplify $$\frac{144}{192}$$.

Answers and Explanations

Easy Level Answers

  1. $$\frac{1}{2}$$ (Divide by 2)
  2. $$\frac{1}{2}$$ (Divide by 3)
  3. $$\frac{1}{2}$$ (Divide by 5)
  4. $$\frac{2}{3}$$ (Divide by 4)
  5. $$\frac{1}{2}$$ (Already in lowest terms)
  6. $$\frac{1}{2}$$ (Divide by 4)
  7. $$\frac{3}{4}$$ (Divide by 3)
  8. $$\frac{2}{3}$$ (Divide by 5)
  9. $$\frac{2}{3}$$ (Divide by 3)
  10. $$\frac{3}{4}$$ (Divide by 6)

Medium Level Answers

  1. $$\frac{3}{4}$$ (Divide by 4)
  2. $$\frac{2}{3}$$ (Divide by 7)
  3. $$\frac{4}{5}$$ (Divide by 5)
  4. $$\frac{2}{5}$$ (Divide by 4)
  5. $$\frac{1}{2}$$ (Divide by 15)
  6. $$\frac{3}{4}$$ (Divide by 9)
  7. $$\frac{2}{3}$$ (Divide by 15)
  8. $$\frac{3}{4}$$ (Divide by 8)
  9. $$\frac{3}{4}$$ (Divide by 12)
  10. $$\frac{1}{2}$$ (Divide by 50)

Hard Level Answers

  1. $$\frac{3}{4}$$ (Divide by 15)
  2. $$\frac{2}{3}$$ (Divide by 28)
  3. $$\frac{7}{9}$$ (Divide by 9)
  4. $$\frac{4}{5}$$ (Divide by 20)
  5. $$\frac{3}{4}$$ (Divide by 24)
  6. $$\frac{3}{5}$$ (Divide by 18)
  7. $$\frac{9}{11}$$ (Divide by 11)
  8. $$\frac{2}{3}$$ (Divide by 44)
  9. $$\frac{2}{5}$$ (Divide by 50)
  10. $$\frac{3}{4}$$ (Divide by 48)

Feel free to ask questions if you’re unsure about anything! Happy learning!