Need more explanation? Explore our learning booklets at Singer Shamrock.
Foundation · Recursive Friendly Decomposition
Make it friendly.
Rebuild the given problem as an easier but equivalent route. Three number fields are available for your shortcut; the fourth field is for the result.
RFD means Recursive Friendly Decomposition: rewrite a calculation using easier numbers without changing its value. You can simplify a difficult step again. Start with addition at level 1; then try the other operations. Higher levels use larger numbers.
How it works — explained step by step
Addition: compensate for rounding
- 48 + 29: replace 29 with 30. That adds 1 too much, so subtract 1.
- 48 + 30 − 1 = 78 − 1 = 77. Enter 48, +, 30, −, 1; result 77.
Subtraction: reverse the correction
- 83 − 29: subtract 30 instead. You have subtracted 1 too much, so add 1 back.
- 83 − 30 + 1 = 53 + 1 = 54.
Multiplication: distribute the factor
- 7 × 28 = 7 × (30 − 2). Multiply both parts by 7.
- 30 × 7 − 14 = 210 − 14 = 196. Do not subtract just 2.
Division: split the dividend
- 156 ÷ 6 = (120 + 36) ÷ 6. Divide both parts by 6.
- 120 ÷ 6 + 6 = 20 + 6 = 26. The last 6 comes from 36 ÷ 6.
With no parentheses, × and ÷ come before + and −; equal-priority operations run left to right. Example: (48 + 12) ÷ 6 = 10, but 48 + 12 ÷ 6 = 50. Select the matching grouping. Any exactly equivalent route is accepted; the checker does not measure how easy it is.