The midpoint is \(\frac{\frac{5}{4}+\frac{9}{4}}{2}=\frac{7}{4}\). The average of two fractions gives the midpoint.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{7}{4}\). The midpoint is \(\frac{\frac{5}{4}+\frac{9}{4}}{2}=\frac{7}{4}\). The average of two fractions gives the midpoint.
Step 3
Exam Tip
मध्य बिंदु \(\frac{\frac{5}{4}+\frac{9}{4}}{2}=\frac{7}{4}\) है। दो भिन्नों का औसत मध्य बिंदु देता है।
The total distance is (2), so each part is \(\frac{2}{8}=\frac{1}{4}\). Find the distance and divide by equal parts.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{4}\). The total distance is (2), so each part is \(\frac{2}{8}=\frac{1}{4}\). Find the distance and divide by equal parts.
Step 3
Exam Tip
कुल दूरी (2) है इसलिए प्रत्येक भाग \(\frac{2}{8}=\frac{1}{4}\) होगा। दूरी निकालकर बराबर भागों से विभाजित करें।
\(\frac{4}{3}\approx1.33\) and \(\sqrt{2}\approx1.41\), so the order is \(\frac{4}{3}<\sqrt{2}<1.5\). Estimate values for comparison.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{4}{3},\sqrt{2},1.5\). \(\frac{4}{3}\approx1.33\) and \(\sqrt{2}\approx1.41\), so the order is \(\frac{4}{3}<\sqrt{2}<1.5\). Estimate values for comparison.
Step 3
Exam Tip
\(\frac{4}{3}\approx1.33\), \(\sqrt{2}\approx1.41\), इसलिए क्रम \(\frac{4}{3}<\sqrt{2}<1.5\) है। तुलना के लिए अनुमान लगाएं।
Each part is \(\frac{3}{12}=\frac{1}{4}\), so the seventh point is \(\frac{7}{4}\). Divide the total length by equal parts.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{7}{4}\). Each part is \(\frac{3}{12}=\frac{1}{4}\), so the seventh point is \(\frac{7}{4}\). Divide the total length by equal parts.
Step 3
Exam Tip
प्रत्येक भाग \(\frac{3}{12}=\frac{1}{4}\) है इसलिए सातवां बिंदु \(\frac{7}{4}\) है। कुल लंबाई को बराबर भागों से बांटें।
The midpoint is \(\frac{\frac{2}{5}+\frac{4}{5}}{2}=\frac{3}{5}\). To find the exact middle point, take the average of the two points.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{5}\). The midpoint is \(\frac{\frac{2}{5}+\frac{4}{5}}{2}=\frac{3}{5}\). To find the exact middle point, take the average of the two points.
Step 3
Exam Tip
मध्य संख्या \(\frac{\frac{2}{5}+\frac{4}{5}}{2}=\frac{3}{5}\) है। दो बिंदुओं के ठीक बीच के लिए उनका औसत लें।
\(\frac{5}{6}\approx0.833\) and \(\frac{7}{8}=0.875\), so \(\frac{7}{8}\) is to the right. Use decimals or cross multiplication to compare.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{7}{8}\). \(\frac{5}{6}\approx0.833\) and \(\frac{7}{8}=0.875\), so \(\frac{7}{8}\) is to the right. Use decimals or cross multiplication to compare.
Step 3
Exam Tip
\(\frac{5}{6}\approx0.833\) और \(\frac{7}{8}=0.875\), इसलिए \(\frac{7}{8}\) दाईं ओर है। तुलना के लिए दशमलव या क्रॉस गुणन करें।
The total length is (2) and there are (8) parts, so each part is \(\frac{2}{8}=\frac{1}{4}\). Divide total length by the number of parts.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{4}\). The total length is (2) and there are (8) parts, so each part is \(\frac{2}{8}=\frac{1}{4}\). Divide total length by the number of parts.
Step 3
Exam Tip
कुल लंबाई (2) है और (8) भाग हैं इसलिए प्रत्येक भाग \(\frac{2}{8}=\frac{1}{4}\) है। बराबर भाग में कुल लंबाई को भागों से बांटें।
B. \(\frac{3}{4}\) और (0.75)/\(\frac{3}{4}\) and (0.75)
Step 1
Concept
\(\frac{3}{4}=0.75\), so both are the same point. Convert forms to identify equal points.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{4}\) और (0.75) / \(\frac{3}{4}\) and (0.75). \(\frac{3}{4}=0.75\), so both are the same point. Convert forms to identify equal points.
Step 3
Exam Tip
\(\frac{3}{4}=0.75\), इसलिए दोनों एक ही बिंदु हैं। समान बिंदु पहचानने के लिए रूप बदलें।
\(\frac{2}{5}\) is greater than (0) and less than (1). In exams, place a proper fraction between (0) and (1).
Step 2
Why this answer is correct
The correct answer is A. (0) और (1) / (0) and (1). \(\frac{2}{5}\) is greater than (0) and less than (1). In exams, place a proper fraction between (0) and (1).
Step 3
Exam Tip
\(\frac{2}{5}\) का मान (0) से अधिक और (1) से कम है। परीक्षा में उचित भिन्न को (0) और (1) के बीच रखें।
\(1.75=1+\frac{3}{4}\), so it lies at the third equal part after (1). Converting decimals to fractions helps locate points easily.
Step 2
Why this answer is correct
The correct answer is C. (1) के बाद तीसरा भाग / Third part after (1). \(1.75=1+\frac{3}{4}\), so it lies at the third equal part after (1). Converting decimals to fractions helps locate points easily.
Step 3
Exam Tip
\(1.75=1+\frac{3}{4}\), इसलिए यह (1) के बाद तीसरे बराबर भाग पर होगा। दशमलव को भिन्न में बदलकर स्थान पहचानना आसान होता है।
\(\frac{3}{4}\) is greater than (0) and less than (1). In exams first compare the fraction value with nearby integers.
Step 2
Why this answer is correct
The correct answer is A. (0) और (1) के बीच / Between (0) and (1). \(\frac{3}{4}\) is greater than (0) and less than (1). In exams first compare the fraction value with nearby integers.
Step 3
Exam Tip
\(\frac{3}{4}\) का मान (1) से कम और (0) से अधिक होता है। परीक्षा में भिन्न की स्थिति पहले उसके मान से पहचानें।
\(\frac{2}{5}=0.4\), \(\frac{1}{2}=0.5\), and \(\frac{3}{5}=0.6\), so \(\frac{1}{2}\) lies between them. Decimal form helps in comparison.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). \(\frac{2}{5}=0.4\), \(\frac{1}{2}=0.5\), and \(\frac{3}{5}=0.6\), so \(\frac{1}{2}\) lies between them. Decimal form helps in comparison.
Step 3
Exam Tip
\(\frac{2}{5}=0.4\), \(\frac{1}{2}=0.5\), और \(\frac{3}{5}=0.6\), इसलिए \(\frac{1}{2}\) बीच में है। तुलना के लिए दशमलव रूप उपयोगी है।
\(\frac{3}{2}=1.5\), so both show the same point. Identify equal values in decimal and fraction forms.
Step 2
Why this answer is correct
The correct answer is A. दोनों बराबर हैं / both are equal. \(\frac{3}{2}=1.5\), so both show the same point. Identify equal values in decimal and fraction forms.
Step 3
Exam Tip
\(\frac{3}{2}=1.5\), इसलिए दोनों एक ही बिंदु दिखाते हैं। दशमलव और भिन्न का समान मान पहचानें।
\(-2+\frac{1}{2}=-\frac{4}{2}+\frac{1}{2}=-\frac{3}{2}\). Be careful with direction when adding a fraction to a negative integer.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{3}{2}\). \(-2+\frac{1}{2}=-\frac{4}{2}+\frac{1}{2}=-\frac{3}{2}\). Be careful with direction when adding a fraction to a negative integer.
Step 3
Exam Tip
\(-2+\frac{1}{2}=-\frac{4}{2}+\frac{1}{2}=-\frac{3}{2}\) है। ऋणात्मक पूर्णांक में भिन्न जोड़ते समय दिशा ध्यान रखें।
\(2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}\). Convert the integer to a fraction with the same denominator.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{9}{4}\). \(2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}\). Convert the integer to a fraction with the same denominator.
Step 3
Exam Tip
\(2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}\) है। पूर्णांक को समान हर वाली भिन्न में बदलें।
A. तीन बराबर भागों में पहला निशान/first mark among three equal parts
Step 1
Concept
For \(\frac{1}{3}\), divide (0) to (1) into (3) equal parts and take the first mark. The denominator tells the number of parts.
Step 2
Why this answer is correct
The correct answer is A. तीन बराबर भागों में पहला निशान / first mark among three equal parts. For \(\frac{1}{3}\), divide (0) to (1) into (3) equal parts and take the first mark. The denominator tells the number of parts.
Step 3
Exam Tip
\(\frac{1}{3}\) के लिए (0) से (1) तक (3) बराबर भाग करें और पहला निशान लें। हर भागों की संख्या बताता है।
The denominator of \(\frac{3}{4}\) is (4), so divide (0) to (1) into (4) equal parts. The numerator tells you to move to the third mark.
Step 2
Why this answer is correct
The correct answer is A. (4). The denominator of \(\frac{3}{4}\) is (4), so divide (0) to (1) into (4) equal parts. The numerator tells you to move to the third mark.
Step 3
Exam Tip
\(\frac{3}{4}\) में हर (4) है, इसलिए (0) से (1) तक (4) बराबर भाग करें। अंश बताता है कि तीसरे निशान पर जाना है।
Here (\left\(\frac{5}{8}\right\)^{-2}=\frac{64}{25}) and (\left\(\frac{8}{5}\right\)^{-2}=\frac{25}{64}). The sum is \(\frac{4096+625}{1600}=\frac{4721}{1600}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{4721}{1600}\). Here (\left\(\frac{5}{8}\right\)^{-2}=\frac{64}{25}) and (\left\(\frac{8}{5}\right\)^{-2}=\frac{25}{64}). The sum is \(\frac{4096+625}{1600}=\frac{4721}{1600}\).
Step 3
Exam Tip
(\left\(\frac{5}{8}\right\)^{-2}=\frac{64}{25}) और (\left\(\frac{8}{5}\right\)^{-2}=\frac{25}{64})। योग \(\frac{4096+625}{1600}=\frac{4721}{1600}\) है।
Since (\left\(\frac{25}{49}\right\)^{\frac{1}{2}}=\frac{5}{7}), (\left\(\frac{25}{49}\right\)^{-\frac{3}{2}}=\left\(\frac{5}{7}\right\)^{-3}=\frac{343}{125}). In exams, take the square root first.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{343}{125}\). Since (\left\(\frac{25}{49}\right\)^{\frac{1}{2}}=\frac{5}{7}), (\left\(\frac{25}{49}\right\)^{-\frac{3}{2}}=\left\(\frac{5}{7}\right\)^{-3}=\frac{343}{125}). In exams, take the square root first.
Step 3
Exam Tip
(\left\(\frac{25}{49}\right\)^{\frac{1}{2}}=\frac{5}{7}), इसलिए (\left\(\frac{25}{49}\right\)^{-\frac{3}{2}}=\left\(\frac{5}{7}\right\)^{-3}=\frac{343}{125})। परीक्षा में पहले वर्गमूल निकालें।
Since (\left\(\frac{81}{256}\right\)^{\frac{1}{4}}=\frac{3}{4}), (\left\(\frac{81}{256}\right\)^{-\frac{3}{4}}=\left\(\frac{3}{4}\right\)^{-3}=\frac{64}{27}). In exams, take the fourth root first.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{64}{27}\). Since (\left\(\frac{81}{256}\right\)^{\frac{1}{4}}=\frac{3}{4}), (\left\(\frac{81}{256}\right\)^{-\frac{3}{4}}=\left\(\frac{3}{4}\right\)^{-3}=\frac{64}{27}). In exams, take the fourth root first.
Step 3
Exam Tip
(\left\(\frac{81}{256}\right\)^{\frac{1}{4}}=\frac{3}{4}), इसलिए (\left\(\frac{81}{256}\right\)^{-\frac{3}{4}}=\left\(\frac{3}{4}\right\)^{-3}=\frac{64}{27})। परीक्षा में पहले चौथा मूल निकालें।
Here (\left\(\frac{4}{7}\right\)^{-2}=\frac{49}{16}) and (\left\(\frac{7}{4}\right\)^{-2}=\frac{16}{49}). The sum is \(\frac{2401+256}{784}=\frac{2657}{784}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{2657}{784}\). Here (\left\(\frac{4}{7}\right\)^{-2}=\frac{49}{16}) and (\left\(\frac{7}{4}\right\)^{-2}=\frac{16}{49}). The sum is \(\frac{2401+256}{784}=\frac{2657}{784}\).
Step 3
Exam Tip
(\left\(\frac{4}{7}\right\)^{-2}=\frac{49}{16}) और (\left\(\frac{7}{4}\right\)^{-2}=\frac{16}{49})। योग \(\frac{2401+256}{784}=\frac{2657}{784}\) है।
Here \(3^{-2}+3^{-4}=\frac{1}{9}+\frac{1}{81}=\frac{10}{81}\), and \(3^{-3}=\frac{1}{27}\). Division gives \(\frac{10}{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{10}{3}\). Here \(3^{-2}+3^{-4}=\frac{1}{9}+\frac{1}{81}=\frac{10}{81}\), and \(3^{-3}=\frac{1}{27}\). Division gives \(\frac{10}{3}\).
Step 3
Exam Tip
\(3^{-2}+3^{-4}=\frac{1}{9}+\frac{1}{81}=\frac{10}{81}\) और \(3^{-3}=\frac{1}{27}\)। भाग देने पर \(\frac{10}{3}\) मिलता है।
Since (\left\(\frac{16}{81}\right\)^{\frac{1}{4}}=\frac{2}{3}), (\left\(\frac{16}{81}\right\)^{-\frac{3}{4}}=\left\(\frac{2}{3}\right\)^{-3}=\frac{27}{8}). In exams, take the fourth root first.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{27}{8}\). Since (\left\(\frac{16}{81}\right\)^{\frac{1}{4}}=\frac{2}{3}), (\left\(\frac{16}{81}\right\)^{-\frac{3}{4}}=\left\(\frac{2}{3}\right\)^{-3}=\frac{27}{8}). In exams, take the fourth root first.
Step 3
Exam Tip
(\left\(\frac{16}{81}\right\)^{\frac{1}{4}}=\frac{2}{3}), इसलिए (\left\(\frac{16}{81}\right\)^{-\frac{3}{4}}=\left\(\frac{2}{3}\right\)^{-3}=\frac{27}{8})। परीक्षा में चौथा मूल पहले निकालें।
