Number Play | IT

Question 20

Observe the figure below. What can you say about the numbers and the lines drawn?

Numbers in the middle column are added in different ways to get the numbers on the sides (1500 + 1500 + 400 = 3400). The numbers in the middle can be used as many times as needed to get the desired sum. Draw arrows from the middle to the numbers on the sides to obtain the desired sums.

Two examples are given. It is simpler to do it mentally!

38,800 = 25,000 + 400 × 2 + 13,000 3400 = 1500 + 1500 + 400

Solution

IT-20

Chapter: NUMBER PLAY
Class: 6 (Class 6)
Category: in_text

Question

Observe the figure below. What can you say about the numbers and the lines drawn?

Two examples are given. It is simpler to do it mentally!

38,800 = 25,000 + 400 × 2 + 13,000 3400 = 1500 + 1500 + 400

Question diagram(s):

Question diagram

Numbers on the sides are sums of middle numbers.

Step 1 — Understanding the rule

We see three columns of numbers. The middle column has numbers. These are 25,000, 400, 13,000, 1,500, 60,000. Side numbers are sums of middle numbers. Middle numbers can be used many times. Let us look at the examples given. For 38,800: $38,800 = 25,000 + (400 \times 2) + 13,000$ $= 25,000 + 800 + 13,000$

$\boxed{38,800}$ This sum uses 25,000, two 400s, 13,000.

For 3,400: $3,400 = (1,500 \times 2) + 400$ $= 3,000 + 400$

$\boxed{3,400}$ This sum uses two 1,500s, one 400.

Step 2 — Finding sums for the left column

Let us find left column sums. For 28,000: $28,000 = 25,000 + (1,500 \times 2)$ $= 25,000 + 3,000$

$\boxed{28,000}$ This sum uses 25,000 and two 1,500s.

For 61,600: $61,600 = 60,000 + (400 \times 4)$ $= 60,000 + 1,600$

$\boxed{61,600}$ This sum uses 60,000 and four 400s.

For 31,000: $31,000 = 25,000 + (1,500 \times 4)$ $= 25,000 + 6,000$

$\boxed{31,000}$ This sum uses 25,000 and four 1,500s.

Diagram 1

Step 3 — Finding sums for the right column

Let us find right column sums. For 63,000: $63,000 = 60,000 + (1,500 \times 2)$ $= 60,000 + 3,000$

$\boxed{63,000}$ This sum uses 60,000 and two 1,500s.

For 19,500: $19,500 = 13,000 + (1,500 \times 3) + (400 \times 5)$ $= 13,000 + 4,500 + 2,000$

$\boxed{19,500}$ This sum uses 13,000, three 1,500s, five 400s.

For 20,900: $20,900 = 13,000 + (1,500 \times 5) + 400$ $= 13,000 + 7,500 + 400$

$\boxed{20,900}$ This sum uses 13,000, five 1,500s, one 400.

Step 4 — Describing the lines drawn

The lines are arrows. Left column arrows point to middle numbers. They show middle numbers used for the sum. Example: 38,800 points to 25,000, 400, 13,000. This means 38,800 is made from these numbers. Middle column arrows point to right numbers. They show middle numbers used for the sum. Example: 1,500 and 400 point to 3,400. This means 3,400 is made from these numbers.

A middle number can be used many times. For example, 38,800 uses two 400s. Only one arrow goes from 38,800 to 400. Also, 3,400 uses two 1,500s. Only one arrow goes from 1,500 to 3,400.

Some diagram arrows are not fully correct. For 3,400, an arrow comes from 25,000. But 25,000 is not part of the sum. For 19,500, arrows come from 13,000 and 1,500. Our sum for 19,500 also uses 400. The arrow from 400 is missing. For 20,900, arrows come from 13,000 and 400. Our sum for 20,900 also uses 1,500. The arrow from 1,500 is missing.

Answer

(i) Numbers in the left and right columns are sums of numbers from the middle column. (ii) Middle column numbers can be used multiple times to form these sums. (iii) Arrows from a left number to middle numbers show its components. (iv) Arrows from middle numbers to a right number show its components. (v) A single arrow represents a component, even if used multiple times. (vi) Some arrows in the diagram are incorrect or some components are missing.

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