Answer :
Certainly! Let's break down each part of the question step-by-step using a tape diagram approach, which helps visualize fractions of a whole.
### a. [tex]\(\frac{1}{4}\)[/tex] of 24
1. Visualize 24: Imagine a tape divided into 4 equal parts since we're finding one-fourth.
2. Find [tex]\(\frac{1}{4}\)[/tex]: Each part represents [tex]\(\frac{1}{4}\)[/tex]. Divide 24 by 4.
3. Result: Each part is worth 6. Therefore, [tex]\(\frac{1}{4}\)[/tex] of 24 is 6.
### b. [tex]\(\frac{1}{4}\)[/tex] of 48
1. Visualize 48: Imagine a tape divided into 4 equal parts.
2. Find [tex]\(\frac{1}{4}\)[/tex]: Divide 48 by 4.
3. Result: Each part is worth 12. Thus, [tex]\(\frac{1}{4}\)[/tex] of 48 is 12.
### c. [tex]\(\frac{2}{3} \times 18\)[/tex]
1. Visualize 18: Imagine splitting a tape into 3 parts.
2. Find 1 part ([tex]\(\frac{1}{3}\)[/tex]): Divide 18 by 3 to find the value of one part.
3. Multiply to find [tex]\(\frac{2}{3}\)[/tex]: Multiply the value of one part by 2.
4. Result: [tex]\(\frac{2}{3}\)[/tex] of 18 is 12.
### d. [tex]\(\frac{2}{6} \times 18\)[/tex]
1. Visualize 18: Imagine a tape divided into 6 parts.
2. Find 1 part ([tex]\(\frac{1}{6}\)[/tex]): Divide 18 by 6 to find the value of one part.
3. Multiply to find [tex]\(\frac{2}{6}\)[/tex]: Multiply the value of one part by 2.
4. Result: [tex]\(\frac{2}{6}\)[/tex] of 18 is 6.
### e. [tex]\(\frac{3}{7} \times 49\)[/tex]
1. Visualize 49: Imagine a tape divided into 7 parts.
2. Find 1 part ([tex]\(\frac{1}{7}\)[/tex]): Divide 49 by 7 to find the value of one part.
3. Multiply to find [tex]\(\frac{3}{7}\)[/tex]: Multiply the value of one part by 3.
4. Result: [tex]\(\frac{3}{7}\)[/tex] of 49 is 21.
### f. [tex]\(\frac{3}{10} \times 120\)[/tex]
1. Visualize 120: Imagine a tape divided into 10 parts.
2. Find 1 part ([tex]\(\frac{1}{10}\)[/tex]): Divide 120 by 10 to find the value of one part.
3. Multiply to find [tex]\(\frac{3}{10}\)[/tex]: Multiply the value of one part by 3.
4. Result: [tex]\(\frac{3}{10}\)[/tex] of 120 is 36.
These visualizations help conceptualize how a fraction represents a part of a whole and how you can calculate it simply by dividing and multiplying.
### a. [tex]\(\frac{1}{4}\)[/tex] of 24
1. Visualize 24: Imagine a tape divided into 4 equal parts since we're finding one-fourth.
2. Find [tex]\(\frac{1}{4}\)[/tex]: Each part represents [tex]\(\frac{1}{4}\)[/tex]. Divide 24 by 4.
3. Result: Each part is worth 6. Therefore, [tex]\(\frac{1}{4}\)[/tex] of 24 is 6.
### b. [tex]\(\frac{1}{4}\)[/tex] of 48
1. Visualize 48: Imagine a tape divided into 4 equal parts.
2. Find [tex]\(\frac{1}{4}\)[/tex]: Divide 48 by 4.
3. Result: Each part is worth 12. Thus, [tex]\(\frac{1}{4}\)[/tex] of 48 is 12.
### c. [tex]\(\frac{2}{3} \times 18\)[/tex]
1. Visualize 18: Imagine splitting a tape into 3 parts.
2. Find 1 part ([tex]\(\frac{1}{3}\)[/tex]): Divide 18 by 3 to find the value of one part.
3. Multiply to find [tex]\(\frac{2}{3}\)[/tex]: Multiply the value of one part by 2.
4. Result: [tex]\(\frac{2}{3}\)[/tex] of 18 is 12.
### d. [tex]\(\frac{2}{6} \times 18\)[/tex]
1. Visualize 18: Imagine a tape divided into 6 parts.
2. Find 1 part ([tex]\(\frac{1}{6}\)[/tex]): Divide 18 by 6 to find the value of one part.
3. Multiply to find [tex]\(\frac{2}{6}\)[/tex]: Multiply the value of one part by 2.
4. Result: [tex]\(\frac{2}{6}\)[/tex] of 18 is 6.
### e. [tex]\(\frac{3}{7} \times 49\)[/tex]
1. Visualize 49: Imagine a tape divided into 7 parts.
2. Find 1 part ([tex]\(\frac{1}{7}\)[/tex]): Divide 49 by 7 to find the value of one part.
3. Multiply to find [tex]\(\frac{3}{7}\)[/tex]: Multiply the value of one part by 3.
4. Result: [tex]\(\frac{3}{7}\)[/tex] of 49 is 21.
### f. [tex]\(\frac{3}{10} \times 120\)[/tex]
1. Visualize 120: Imagine a tape divided into 10 parts.
2. Find 1 part ([tex]\(\frac{1}{10}\)[/tex]): Divide 120 by 10 to find the value of one part.
3. Multiply to find [tex]\(\frac{3}{10}\)[/tex]: Multiply the value of one part by 3.
4. Result: [tex]\(\frac{3}{10}\)[/tex] of 120 is 36.
These visualizations help conceptualize how a fraction represents a part of a whole and how you can calculate it simply by dividing and multiplying.
