Question

1. amanda is planning a graduation party for her son, who has just finished 5th grade. she has a party budget that is broken down into 5 categories: venue, invitations, food, entertainment, and decorations. amanda wants to spend \\(\frac{6}{24}\\) of her budget on the venue, \\(\frac{1}{10}\\) on invitations, \\(\frac{1}{4}\\) on food, \\(\frac{3}{10}\\) on decorations, and the rest of her budget on entertainment. what fraction of amandas budget can she spend on entertainment?

Explanation:

Step1: Find a common denominator

The denominators are 24, 10, 4, and 10. The least common multiple of 24, 10, and 4 is 120.

Step2: Convert each fraction to have denominator 120

• For venue: $\frac{6}{24}=\frac{6\times5}{24\times5}=\frac{30}{120}$
• For invitations: $\frac{1}{10}=\frac{1\times12}{10\times12}=\frac{12}{120}$
• For food: $\frac{1}{4}=\frac{1\times30}{4\times30}=\frac{30}{120}$
• For decorations: $\frac{3}{10}=\frac{3\times12}{10\times12}=\frac{36}{120}$

Step3: Sum the fractions of the known categories

$\frac{30}{120}+\frac{12}{120}+\frac{30}{120}+\frac{36}{120}=\frac{30 + 12+30 + 36}{120}=\frac{108}{120}$

Step4: Subtract the sum from 1 (the whole budget) to find the fraction for entertainment

$1-\frac{108}{120}=\frac{120}{120}-\frac{108}{120}=\frac{120 - 108}{120}=\frac{12}{120}=\frac{1}{10}$

Answer:

$\frac{1}{10}$