Write the next 2 rational numbers to complete the patter given below
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-16/14
-24/21
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Answers
Answer:
(i)
Given, numbers are −1 and 0.
Write −1 and 0as a rational number with denominator 6.
Now, the rational number becomes,
−1=−66 and 0=06
Now, we write the number between −66 and 06.
−66<−56<−46<−36<−26<−16<06−1<−56<−46<−36<−26<−16<0−1<−56<−23<−12<−13<−16<0
Thus, the five rational number between −1 and 0 are −56,−23,−12,−13,−16.
(ii)
Given, number are −2 and −1.
Write −1 and 0as a rational number with denominator 6.
Now, the rational number becomes,
−2=−126 and −1=−66
Now, we write the number between −126 and −66.
−126<−116<−106<−96<−86<−76<−66−2<−116<−106<−96<−86<−76<−1−2<−116<−53<−32<−43<−76<−1
Thus, the five rational number between −2 and −1 are −116,−53,−32,−43,−76.
(iii)
Given that the rational number is −45 and −23.
Write −45 and −23as a rational number with denominator 45.
Now, the rational number becomes,
−4×95×9=−3645 and −2×153×15=−3045
Now, we write the number between −3645 and −3045.
−3645<−3545<−3435<−3345<−3245<−3145<−3045−45<−3545<−3435<−3345<−3245<−3145<−23−45<−79<−3435<−3345<−3245<−3145<−23
Thus, the five rational number between −45 and −23 are −79,−3435,−3345,−3245,−3145.
(iv)
Given, number are 12 and 23.
Write −12 and 23as a rational number with denominator 36.
Now, the rational number becomes,
1×182×18=1836 and 2×123×12=2436
Now, we write the number between 36 and 46.
1836<1936<2036<2136<2236<2336<243612<1936<59<712<1113<2336<23
Thus, the five rational number between −12 and 23 are 1936,59,712,1113,2336.
Question 2
Write four more rational numbers in each of the following patterns: (i) -3/ 5, -6/10, -9/15, -12/20 ,........... (ii)-1/4 ,-2/8, -3/12 ,..... (iii) -1/6,2/ -12,3/-18,4/-24,...... (iv)-2/3,2/-3,4/-6,6/-9,….
Answer:
(i)
Given, rational numbers are −35,−610,−915,−1220
The pattern of the above rational numbers is,
−35=−3×15×1,−610=−3×25×2,−915=−3×35×3,−1220=−3×45×4
The next four rational numbers according to above pattern are,
−3×55×5,−3×65×6,−3×75×7,−3×85×8−1525,−1830,−2135,−2440
(ii)
Given, rational numbers are −14,−28,−312.
The pattern of the above rational numbers is,
−14=−1×14×1,−28=−1×24×2,−312=−1×34×3
The next four rational numbers according to above pattern are,
−1×44×4,−1×54×5,−1×64×6,−1×74×7−416,−520,−624,−728
(iii)
Given, rational numbers are −16,2−12,3−18,4−24.
The pattern of the above rational numbers is,
−16=−1×16×1,2−12=1×2−6×2,3−18=3×1−6×3,4−24=4×1−6×4
The next four rational numbers according to above pattern are,
1×5−6×5,1×6−6×6,1×7−6×7,1×8−6×85−30,6−36,7−42,8−48
Step-by-step explanation:
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