Original independent learning guide. Not official KICD content.
Make equivalence visible
Draw two rectangles of the same size. Divide the first into four equal parts and shade three. Divide the second into eight equal parts and shade six. The shaded amounts match, so three quarters equals six eighths. Multiply both the numerator and denominator by the same non-zero number to produce equivalent fractions. Changing only one of them changes the amount. Use the drawing to explain the rule before relying on it in a calculation.
Worked example: add unlike fractions
To calculate 3/4 + 1/6, use twelfths because both 4 and 6 divide into 12. Write 3/4 as 9/12 and 1/6 as 2/12. Adding the numerators gives 11/12. The denominator stays 12 because the parts are still twelfths. Check the size: three quarters plus a sixth is larger than three quarters but less than a whole. An answer of 4/10 would fail this check.
Mixed numbers and subtraction
A mixed number combines whole units with a fraction. For 2 1/3 minus 3/4, rewrite 2 1/3 as 7/3, then use twelfths: 28/12 minus 9/12 equals 19/12, or 1 7/12. Alternatively, separate one whole into twelfths before subtracting. Keep track of each whole rather than subtracting the fractional parts without regrouping. Explain which method you chose and why it preserves the original quantity.
A short revision routine for home or class
Spend a few minutes drawing one equivalent pair, then attempt the questions independently. Write each conversion on a separate line. Ask a partner to explain what the denominator represents without looking at your answer. Use the explanations below after your attempt and record the reason for any correction. For a teacher, a useful exit question changes the numbers but keeps the same method; it checks understanding rather than recall of one worked answer.
Practice questions
Write 2/3 in twelfths.
Calculate 1/2 + 2/5.
Calculate 1 1/4 minus 1/2.
Answers and explanations
Multiply numerator and denominator by 4: 2/3 = 8/12.
Use tenths: 5/10 + 4/10 = 9/10.
Convert to quarters: 5/4 minus 2/4 = 3/4.
