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PIT_PIT [208]
3 years ago
8

Showing A Tape Diagram to solve 2/3 of 5 Equalling the Answer, Thank You.

Mathematics
1 answer:
Fittoniya [83]3 years ago
6 0

Answer:

see the explanation

Step-by-step explanation:

we know that

A<u><em> tape diagram</em></u> is a visual model that looks like a segment of tape and is used for representing number relationships and word problems

we have that

5(\frac{2}{3})=\frac{10}{3}

The expression 5(\frac{2}{3})  can be thought of as" five groups of two-thirds"

see the attached figure N 1

so

5(\frac{2}{3})=\frac{2}{3}+\frac{2}{3}+\frac{2}{3}+\frac{2}{3}+\frac{2}{3}=\frac{10}{3}

Another way to solve

The expression 5(\frac{2}{3})  can be thought of as" ten groups of one-thirds"

see the attached figure N 2

so

5(\frac{2}{3})=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{10}{3}

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Sterre charges $ 3 5 $35dollar sign, 35 to file tax returns, but files for free if she only needs the easiest form. Then she don
blagie [28]

Given:

  • $35 is charged per form, but $0 if only the easiest form is filed.
  • $2 donated for every single tax return filed (since it is not explicitly mentioned otherwise, I will assume she donates $2 whether she charges $35 or does it for free)
  • Total amount charged for the full year = $7245
  • Total amount donated for the full year = $1242

To Find: The number of forms for which Sterre charged $35 and the number of forms Sterre did it for free.

Concept:

We can make use of the Unitary Method here. <u>Given the number of units in a group, the Unitary Method can be used to find the value of a single unit or and individual unit when we are given the value for a group.</u>

So,

<u>Value of Single Unit = Value of Entire Group of Units ÷ Number of Units in the Group</u>


Explanation & Calculation:

We are given that Sterre charged $7245 for the full year. Taking each Unit as the $35 type of form, and value of each Unit would be the amount that Sterre charges per form which is obviously $35, we can find the number of $35 forms using the expression written above.

So, putting in the values into the expression,

$35 = $7245 ÷ number of $35 forms

Therefore, number of $35 forms = $7245 ÷ $35

Using simple division, number of $35 forms = 207

Next, we are given Sterre donated $1242 in the full year and she donates $2 for every form (whether it is the $35 form or the free form).

If this time, we define each Unit as being each form (both $35 form and free form), value of each unit we define as the $2 donation money, we see that the value of the full group of units is $1242.

So, putting the values into the expression,

$2 = $1242 ÷ total number of forms

Therefore, total number of forms = $1242 ÷ $2

Using simple division, total number of forms = 621


Conclusion:

Sterre has filed <u>a total of 621 tax returns</u> (both charged and for free).

Of these 621 returns filed, <u>for 207 forms, Sterre charged $35</u>.

The number of returns Sterre filed for free (that is, the easiest forms) is

Total number of forms - Chargeable forms = 621 - 207 = 414

Thus, Sterre filed <u>414 tax returns for free</u>.


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