We read your photo as:

Write if true or false. A. The cost of 16 pineapples is ₹432. So, the cost of 1 pineapple is ₹26. B. 15 bottles of juice cost ₹225. The cost of 1 bottle of juice is ₹15.

Mathematics

ScanSolve AI Answer

Step-by-step solution

29 steps

Lesson 1: Introducing Proportion

1. Fill in the blanks.

  • A. The simplest form of the ratio 24:72 is
  1. Find the greatest common divisor (GCD) of 24 and 72.

    $$
    24 = 24 \times 1
    $$
    $$
    72 = 24 \times 3
    $$
    The GCD is 24.
    
  2. Divide both parts of the ratio by the GCD.

    $$
    \frac{24}{24} : \frac{72}{24} = 1:3
    $$
    The simplest form is $\boxed{\text{1:3}}$.
    
    • B. 81:153 in its simplest form is
  3. Find the GCD of 81 and 153.

    $$
    81 = 9 \times 9
    $$
    $$
    153 = 9 \times 17
    $$
    The GCD is 9.
    
  4. Divide both parts of the ratio by the GCD.

    $$
    \frac{81}{9} : \frac{153}{9} = 9:17
    $$
    The simplest form is $\boxed{\text{9:17}}$.
    
    • C. The simplest form of 132:33 is
  5. Find the GCD of 132 and 33.

    $$
    132 = 33 \times 4
    $$
    $$
    33 = 33 \times 1
    $$
    The GCD is 33.
    
  6. Divide both parts of the ratio by the GCD.

    $$
    \frac{132}{33} : \frac{33}{33} = 4:1
    $$
    The simplest form is $\boxed{\text{4:1}}$.
    

    2. Write if the ratios are in proportion or not.
    To check for proportion, we compare the simplified forms of the ratios or cross-multiply.

    • A. 15:45 and 21:63
  7. Simplify the first ratio.

    $$
    \frac{15}{45} = \frac{1}{3}
    $$
    
  8. Simplify the second ratio.

    $$
    \frac{21}{63} = \frac{1}{3}
    $$
    Since $\frac{1}{3} = \frac{1}{3}$, the ratios are in proportion.  
    The ratios are $\boxed{\text{in proportion}}$.
    
    • B. 14:15 and 56:60
  9. Simplify the first ratio.

    $$
    \frac{14}{15}
    $$
    This ratio is already in simplest form.
    
  10. Simplify the second ratio.

    $$
    \frac{56}{60} = \frac{56 \div 4}{60 \div 4} = \frac{14}{15}
    $$
    Since $\frac{14}{15} = \frac{14}{15}$, the ratios are in proportion.  
    The ratios are $\boxed{\text{in proportion}}$.
    
    • C. 20 L:100 mL and 50 L:250 L
  11. Convert units for the first ratio to be consistent.

    1 L=1000 mL1 \text{ L} = 1000 \text{ mL}. 20 L:100 mL=(20×1000) mL:100 mL=20000 mL:100 mL 20 \text{ L} : 100 \text{ mL} = (20 \times 1000) \text{ mL} : 100 \text{ mL} = 20000 \text{ mL} : 100 \text{ mL} Simplify the first ratio. 20000100=2001 \frac{20000}{100} = \frac{200}{1}

  12. Simplify the second ratio.

    $$
    \frac{50 \text{ L}}{250 \text{ L}} = \frac{50 \div 50}{250 \div 50} = \frac{1}{5}
    $$
    Since $\frac{200}{1} \neq \frac{1}{5}$, the ratios are not in proportion.  
    The ratios are $\boxed{\text{not in proportion}}$.
    
    • D. 65 people:35 people and ₹600:₹300
  13. Simplify the first ratio.

    $$
    \frac{65}{35} = \frac{65 \div 5}{35 \div 5} = \frac{13}{7}
    $$
    
  14. Simplify the second ratio.

    $$
    \frac{600}{300} = \frac{2}{1}
    $$
    Since $\frac{13}{7} \neq \frac{2}{1}$, the ratios are not in proportion.  
    The ratios are $\boxed{\text{not in proportion}}$.
    

    3. Ryan bought 16 bananas for ₹120 and Kate bought 18 bananas for ₹144. Did they buy the bananas at the same price? Write yes or no.

  15. Calculate the price per banana for Ryan.

    Ryan’s price per banana=Total costNumber of bananas=₹12016 bananas=₹7.50 per banana\text{Ryan's price per banana} = \frac{\text{Total cost}}{\text{Number of bananas}} = \frac{₹120}{16 \text{ bananas}} = ₹7.50 \text{ per banana}
  16. Calculate the price per banana for Kate.

    Kate’s price per banana=Total costNumber of bananas=₹14418 bananas=₹8.00 per banana\text{Kate's price per banana} = \frac{\text{Total cost}}{\text{Number of bananas}} = \frac{₹144}{18 \text{ bananas}} = ₹8.00 \text{ per banana}
  17. Compare the prices.

    Since ₹7.50 ≠\neq ₹8.00, they did not buy the bananas at the same price.
    The answer is no\boxed{\text{no}}.

    Lesson 2: Proportional Terms

    1. Write 3 equivalent ratios for 7:12.
    To find equivalent ratios, multiply both terms by the same non-zero number.

  18. Multiply by 2.

    7×2:12×2=14:247 \times 2 : 12 \times 2 = 14:24
  19. Multiply by 3.

    7×3:12×3=21:367 \times 3 : 12 \times 3 = 21:36
  20. Multiply by 4.

    7×4:12×4=28:487 \times 4 : 12 \times 4 = 28:48

    Three equivalent ratios are 14:24, 21:36, 28:48\boxed{\text{14:24, 21:36, 28:48}}.

    2. Find out if the ratios are in proportion by comparing the product of the means and the product of the extremes. If they are, write them in proportion.
    For a:b::c:da:b::c:d, they are in proportion if ad=bcad = bc.

    • A. 7:14 and 6:12
  21. Identify extremes and means.

    Extremes are 7 and 12. Means are 14 and 6.

  22. Calculate the product of the extremes.

    $$
    7 \times 12 = 84
    $$
    
  23. Calculate the product of the means.

    $$
    14 \times 6 = 84
    $$
    Since $84 = 84$, the ratios are in proportion.  
    In proportion: $\boxed{7:14::6:12}$.
    
    • B. 5:8 and 25:40
  24. Identify extremes and means.

    Extremes are 5 and 40. Means are 8 and 25.

  25. Calculate the product of the extremes.

    $$
    5 \times 40 = 200
    $$
    
  26. Calculate the product of the means.

    $$
    8 \times 25 = 200
    $$
    Since $200 = 200$, the ratios are in proportion.  
    In proportion: $\boxed{5:8::25:40}$.
    
    • C. 9:12 and 99:112
  27. Identify extremes and means.

    Extremes are 9 and 112. Means are 12 and 99.

  28. Calculate the product of the extremes.

    $$
    9 \times 112 = 1008
    $$
    
  29. Calculate the product of the means.

    $$
    12 \times 99 = 1188
    $$
    Since $1008 \neq 1188$, the ratios are not in proportion.  
    The ratios are
    
Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp