Answered

IDNLearn.com: Your one-stop platform for getting reliable answers to any question. Our experts provide timely and accurate responses to help you navigate any topic or issue with confidence.

Fill in the following:

(a) [tex]$7 \div \frac{3}{5} =$[/tex]

(b) [tex]$3 \frac{1}{2} \div \frac{1}{21} =$[/tex]

(c) [tex]$\frac{5}{7} \div \frac{10}{21} =$[/tex]

(d) [tex]$5 \frac{5}{6} \div \frac{5}{6} =$[/tex]

(e) [tex]$3 \div \frac{3}{5} =$[/tex]

(f) [tex]$6 \frac{1}{2} \div 1 \frac{3}{8} =$[/tex]

(g) [tex]$83 \div 83 =$[/tex]

Sagot :

GinnyAnsweridn
Sure! Let's solve each of these division problems step by step.

### (a) [tex]\[7 \div \frac{3}{5}\][/tex]

1. When dividing by a fraction, we multiply by its reciprocal.
2. [tex]\[7 \div \frac{3}{5} = 7 \times \frac{5}{3} = \frac{7 \times 5}{3} = \frac{35}{3} \approx 11.666666666666668\][/tex]

### (b) [tex]\[3 \frac{1}{2} \div \frac{1}{21}\][/tex]

1. Convert the mixed number to an improper fraction.
2. [tex]\[3 \frac{1}{2} = \frac{7}{2}\][/tex]
3. When dividing by a fraction, we multiply by its reciprocal.
4. [tex]\[\frac{7}{2} \div \frac{1}{21} = \frac{7}{2} \times 21 = \frac{7 \times 21}{2} = \frac{147}{2} = 73.5\][/tex]

### (c) [tex]\[\frac{5}{7} \div \frac{10}{21}\][/tex]

1. When dividing by a fraction, we multiply by its reciprocal.
2. [tex]\[\frac{5}{7} \div \frac{10}{21} = \frac{5}{7} \times \frac{21}{10} = \frac{5 \times 21}{7 \times 10} = \frac{105}{70} = \frac{3}{2} = 1.5\][/tex]

### (d) [tex]\[5 \frac{5}{6} \div \frac{5}{6}\][/tex]

1. Convert the mixed number to an improper fraction.
2. [tex]\[5 \frac{5}{6} = \frac{35}{6}\][/tex]
3. When dividing by a fraction, we multiply by its reciprocal.
4. [tex]\[\frac{35}{6} \div \frac{5}{6} = \frac{35}{6} \times \frac{6}{5} = \frac{35 \times 6}{6 \times 5} = \frac{210}{30} = 7\][/tex]

### (e) [tex]\[3 \div \frac{3}{5}\][/tex]

1. When dividing by a fraction, we multiply by its reciprocal.
2. [tex]\[3 \div \frac{3}{5} = 3 \times \frac{5}{3} = \frac{3 \times 5}{3} = 5\][/tex]

### (f) [tex]\[6 \frac{1}{2} \div 1 \frac{3}{8}\][/tex]

1. Convert the mixed numbers to improper fractions.
2. [tex]\[6 \frac{1}{2} = \frac{13}{2}\][/tex]
3. [tex]\[1 \frac{3}{8} = \frac{11}{8}\][/tex]
4. When dividing by a fraction, we multiply by its reciprocal.
5. [tex]\[\frac{13}{2} \div \frac{11}{8} = \frac{13}{2} \times \frac{8}{11} = \frac{13 \times 8}{2 \times 11} = \frac{104}{22} \approx 4.7272727272727275\][/tex]

### (g) [tex]\[83 \div 83\][/tex]

1. Dividing a number by itself gives us [tex]\(1\)[/tex].
2. [tex]\[83 \div 83 = 1\][/tex]

These detailed solutions match the numerical results provided.
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.