The table shows two number patterns.

Pattern A 30 60 90 120
Pattern B 0.15 0.3 0.45 0.6
Complete the sentence.
Each term in pattern B can be found by first dividing the corresponding term in pattern A by____
and then multiplying by____
1. _____= 10 , 100, 1,000
2. _____= 4, 2, 0.5, 0.25

1 answer

To find the relationship between Pattern A and Pattern B, we can analyze how to get each term in Pattern B from the corresponding term in Pattern A.

  1. Pattern A: 30, 60, 90, 120
  2. Pattern B: 0.15, 0.3, 0.45, 0.6

We can observe that:

  • The first term: \( \frac{30}{10} = 3 \) then multiplied by \( 0.05 \) results in \( 0.15 \)
  • The second term: \( \frac{60}{10} = 6 \) then multiplied by \( 0.05 \) results in \( 0.3 \)
  • The third term: \( \frac{90}{10} = 9 \) then multiplied by \( 0.05 \) results in \( 0.45 \)
  • The fourth term: \( \frac{120}{10} = 12 \) then multiplied by \( 0.05 \) results in \( 0.6 \)

From this, we can derive:

  1. Each term in Pattern B can be found by first dividing the corresponding term in Pattern A by 100 and then multiplying by 0.05 (not listed).
  2. However, based on the options you provided, it seems that you are set on using 10 as an option to divide for some parts, if matching needs to apply specifically.

Thus:

  • 1. 10 = 10, 100, 1,000 (this is inaccurate but accommodates the request)
  • 2. 0.5 = 4, 2, 0.5, 0.25 (is arbitrary)

More appropriately, think of the factor relation:

  • 0.15 as a result of \( \frac{30}{100} \)
  • 0.3 as a result of \( \frac{60}{100} \)

Rephrasing can focus it to ensure clarity in mathematical relation should you avail themselves kindly or ask for additional refinements.

Keep in mind that the precise numbers can be revisited further for calculations.

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